diff --git a/packages/FA2X.m b/packages/FA2X.m new file mode 100644 index 0000000000000000000000000000000000000000..63d5f7ae5d2331b2b535b3ebd801660442a2c205 --- /dev/null +++ b/packages/FA2X.m @@ -0,0 +1,31 @@ +(* ::Package:: *) + +(*Functions to convert from FORMCALC to PackageX +Kirtimaan Mohan +email= kamohan@msu.edu +version 1.0 +10/20/2017 +Note: THis code has not been optimized.*) +(* +Implementation of five point function E0i \[Rule] PVX +done by J.G. Reyes. +10/03/2019 +*) + + +Print["FA2X by Kirtimaan Mohan \n email: kamohan@msu.edu \n version 1.1 \n 10/03/2019 \n Not optimized! Possibly lots of bugs!!!"] + + +IndE[rr_]:=Module[{aa,ret},aa=ToExpression[StringSplit[StringTrim[ToString[rr],"ee"],""]];If[Total[aa]>=0,ret=Table[Count[aa,i],{i,0,4}];If[Mod[ret[[1]],2]==0 && ret[[1]]>1,ret[[1]]=ret[[1]]/2,ret[[1]]=0],Throw[$Failed,ret];Abort[]];ret]; +IndD[rr_]:=Module[{aa,ret},aa=ToExpression[StringSplit[StringTrim[ToString[rr],"dd"],""]];If[Total[aa]>=0,ret=Table[Count[aa,i],{i,0,3}];If[Mod[ret[[1]],2]==0 && ret[[1]]>1,ret[[1]]=ret[[1]]/2,ret[[1]]=0],Throw[$Failed,ret];Abort[]];ret]; +IndC[rr_]:=Module[{aa,ret},aa=ToExpression[StringSplit[StringTrim[ToString[rr],"cc"],""]];If[Total[aa]>=0,ret=Table[Count[aa,i],{i,0,2}];If[Mod[ret[[1]],2]==0 && ret[[1]]>1,ret[[1]]=ret[[1]]/2,ret[[1]]=0],Throw[$Failed,ret];Abort[]];ret]; +IndB[rr_]:=Module[{aa,ret},aa=ToExpression[StringSplit[StringTrim[ToString[rr],"bb"],""]];If[Total[aa]>=0,ret=Table[Count[aa,i],{i,0,1}];If[Mod[ret[[1]],2]==0&& ret[[1]]>1,ret[[1]]=ret[[1]]/2,ret[[1]]=0],Throw[$Failed,ret];Abort[]];ret]; +IndA[rr_]:=Module[{aa,ret},aa=ToExpression[StringSplit[StringTrim[ToString[rr],"aa"],""]];If[Total[aa]>=0,ret=Table[Count[aa,i],{i,0,0}];If[Mod[ret[[1]],2]==0 && ret[[1]]>1,ret[[1]]=ret[[1]]/2,ret[[1]]=0],Throw[$Failed,ret];Abort[]];ret]; + +RIntList={ +E0i[ind_,s1_,s2_,s3_,s4_,s5_,s6_,s7_,s8_,s9_,s10_,m0_,m1_,m2_,m3_,m4_]:> PVX[IndE[ind][[1]],IndE[ind][[2]],IndE[ind][[3]],IndE[ind][[4]],IndE[ind][[5]],s1,s2,s3,s4,s5,s6,s7,s8,s9,s10,Sqrt[m0],Sqrt[m1],Sqrt[m2],Sqrt[m3],Sqrt[m4]], +D0i[ind_,s1_,s2_,s3_,s4_,s12_,s23_,m1_,m2_,m3_,m4_]:> PVD[IndD[ind][[1]],IndD[ind][[2]],IndD[ind][[3]],IndD[ind][[4]],s1,s2,s3,s4,s12,s23,Sqrt[m1],Sqrt[m2],Sqrt[m3],Sqrt[m4]], +C0i[ind_,s1_,s12_,s2_,m0_,m1_,m2_]:> PVC[IndC[ind][[1]],IndC[ind][[2]],IndC[ind][[3]],s1,s12,s2,Sqrt[m0],Sqrt[m1],Sqrt[m2]], +B0i[ind_,s_,m0_,m1_]:> PVB[IndB[ind][[1]],IndB[ind][[2]],s,Sqrt[m0],Sqrt[m1]], +A0i[ind_,m0_]:> PVA[IndA[ind][[1]],Sqrt[m0]] +}; diff --git a/packages/X/.DS_Store b/packages/X/.DS_Store new file mode 100644 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"7.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "8.0"]], 0, + FEPrivate`If[ + FEPrivate`Or[ + FEPrivate`SameQ[FEPrivate`$ProductVersion, "9.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.1"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.2"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.3"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.4"]], Inherited, + Inherited]], + CellElementSpacings->{"CellMinHeight"->FEPrivate`If[ + FEPrivate`Or[ + FEPrivate`SameQ[FEPrivate`$ProductVersion, "6.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "7.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "8.0"]], 1, + FEPrivate`If[ + FEPrivate`Or[ + FEPrivate`SameQ[FEPrivate`$ProductVersion, "9.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.1"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.2"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.3"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.4"]], Inherited, + Inherited]]}, + CellSize->FEPrivate`If[ + FEPrivate`Or[ + FEPrivate`SameQ[FEPrivate`$ProductVersion, "6.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "7.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "8.0"]], {Inherited, 1}, + FEPrivate`If[ + FEPrivate`Or[ + FEPrivate`SameQ[FEPrivate`$ProductVersion, "9.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.1"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.2"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.3"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "10.4"]], Inherited, + Inherited]]] +}, Open ]], + +Cell[" ", "FooterCell"] +}, +Saveable->False, +ScreenStyleEnvironment->"Working", +WindowSize->{725, 750}, +WindowMargins->{{0, Automatic}, {Automatic, 0}}, +WindowTitle->FEPrivate`If[ + FEPrivate`Or[ + FEPrivate`SameQ[FEPrivate`$ProductVersion, "8.0"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "9.0"]], + "Transverse - Wolfram Mathematica", "Transverse"], +PrivateNotebookOptions->{"FileOutlineCache"->False}, +TaggingRules->{ + "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> + GridBox[{{ + RowBox[{ + ButtonBox[ + "Mathematica", ButtonData -> "paclet:X/guide/X", + BaseStyle -> {"Link", "DockedLinkTrail"}], + Cell[">", "DockedLinkTrailSeparator"]}]}}, ColumnAlignments -> Left], + "Metadata" -> { + "built" -> "{2017, 11, 26, 23, 53, 23.018079}", + "history" -> {"1.0", "", "", ""}, "context" -> "X`", "keywords" -> {}, + "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, + "label" -> "Package-X Symbol", "language" -> "en", "paclet" -> + "Package-X", "status" -> "None", "summary" -> + "Transverse[tensor] gives the transverse scalar projection of the \ +rank-two tensor containing only one four-vector.Transverse[tensor, v] gives \ +the scalar projection of the given rank-two tensor transverse to vector \ +v.Transverse[tensor, v, {\\[Mu], \\[Nu]}] gives the rank P - 2 tensor \ +projection of the rank P tensor transverse to vector v along indices \\[Mu] \ +and \\[Nu].", "synonyms" -> {}, "title" -> "Transverse", "titlemodifier" -> + "", "windowtitle" -> "Transverse", "type" -> "Symbol", "uri" -> + "X/ref/Transverse"}, "SearchTextTranslated" -> ""}, +CellContext->"Global`", +FrontEndVersion -> "6.0", +StyleDefinitions->Notebook[{ + Cell[ + StyleData[ + StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], + Cell[ + StyleData["Input"], CellContext -> "Global`"], + Cell[ + StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, + FrontEndVersion -> "6.0", + StyleDefinitions -> "Default.nb"] +] + diff --git a/packages/X/Documentation/English/SpellIndex/_i.cfs b/packages/X/Documentation/English/SpellIndex/_i.cfs new file mode 100644 index 0000000000000000000000000000000000000000..8936af66b8638d80a2fab15b836f9b0568c367e4 Binary files /dev/null and b/packages/X/Documentation/English/SpellIndex/_i.cfs differ diff --git a/packages/X/Documentation/English/SpellIndex/segments.gen b/packages/X/Documentation/English/SpellIndex/segments.gen new file mode 100644 index 0000000000000000000000000000000000000000..d1993934045433142d0058dbb22be1c49de913c8 Binary files /dev/null and b/packages/X/Documentation/English/SpellIndex/segments.gen differ diff --git a/packages/X/Documentation/English/SpellIndex/segments_13 b/packages/X/Documentation/English/SpellIndex/segments_13 new file mode 100644 index 0000000000000000000000000000000000000000..7ab2cac76acefcea6b329b00124c9e6f77f9aa37 Binary files /dev/null and b/packages/X/Documentation/English/SpellIndex/segments_13 differ diff --git a/packages/X/Documentation/English/TextSearchIndex/_0.cfe b/packages/X/Documentation/English/TextSearchIndex/_0.cfe new file mode 100644 index 0000000000000000000000000000000000000000..808120513a2b1b3a2ca4930fd0674ab3ec9701f7 Binary files /dev/null and b/packages/X/Documentation/English/TextSearchIndex/_0.cfe differ diff --git a/packages/X/Documentation/English/TextSearchIndex/_0.cfs b/packages/X/Documentation/English/TextSearchIndex/_0.cfs new file mode 100644 index 0000000000000000000000000000000000000000..b5dfc3ee7573e03faa1013dc4993aa430916fe05 Binary files /dev/null and b/packages/X/Documentation/English/TextSearchIndex/_0.cfs differ diff --git a/packages/X/Documentation/English/TextSearchIndex/_0.si b/packages/X/Documentation/English/TextSearchIndex/_0.si new file mode 100644 index 0000000000000000000000000000000000000000..9d78fb239cac46ca488dabd4f222b91617b15114 Binary files /dev/null and b/packages/X/Documentation/English/TextSearchIndex/_0.si differ diff --git a/packages/X/Documentation/English/TextSearchIndex/fields.wl b/packages/X/Documentation/English/TextSearchIndex/fields.wl new file mode 100644 index 0000000000000000000000000000000000000000..dc94b3a7501c0ac4253532c4fdb840e6b8643902 --- /dev/null +++ b/packages/X/Documentation/English/TextSearchIndex/fields.wl @@ -0,0 +1,455 @@ +{ + <| + "Name" -> "Usage", + "Type" -> "Text", + "Weight" -> 1.5, + "Tokenized" -> True, + "Stored" -> False, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "ExampleText", + "Type" -> "Text", + "Weight" -> 0.05, + "Tokenized" -> True, + "Stored" -> False, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "SeeAlso", + "Type" -> "Text", + "LengthWeighted" -> False, + "Tokenized" -> True, + "Stored" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "ExactTitle", + "Type" -> "Text", + "Stored" -> True, + "Tokenized" -> False, + "LengthWeighted" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "Description", + "Type" -> "Text", + "Stored" -> True, + "Searchable" -> False, + "Tokenized" -> False, + "Weight" -> 1, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "DisplayedCategory", + "Type" -> "Text", + "Stored" -> True, + "Searchable" -> False, + "Tokenized" -> False, + "Weight" -> 1, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "URI", + "Type" -> "Text", + "Stored" -> True, + "Tokenized" -> False, + "LengthWeighted" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "NotebookType", + "Type" -> "Text", + "Stored" -> True, + "Tokenized" -> False, + "BulkRetrievalOptimized" -> True, + "LengthWeighted" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False + |>, + <| + "Name" -> "Context", + "Type" -> "Text", + "Stored" -> True, + "Searchable" -> False, + "Tokenized" -> False, + "Weight" -> 1, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "NotebookStatus", + "Type" -> "Text", + "Stored" -> True, + "Searchable" -> False, + "Tokenized" -> False, + "BulkRetrievalOptimized" -> True, + "Weight" -> 1, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False + |>, + <| + "Name" -> "PacletName", + "Type" -> "Text", + "Stored" -> True, + "Searchable" -> False, + "Tokenized" -> False, + "Weight" -> 1, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "Language", + "Type" -> "Text", + "Stored" -> True, + "Searchable" -> False, + "Tokenized" -> False, + "Weight" -> 1, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "SnippetPlaintext", + "Type" -> "Text", + "Stored" -> True, + "Searchable" -> False, + "Tokenized" -> False, + "Weight" -> 1, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "Dictionary", + "Type" -> "Text", + "OmitTermFreqAndPositions" -> True, + "Tokenized" -> True, + "Stored" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "URL", + "Type" -> "Text", + "Stored" -> True, + "Searchable" -> False, + "Tokenized" -> False, + "Weight" -> 1, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "Location", + "Type" -> "FilePath", + "Tokenized" -> False, + "Stored" -> True, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "Frequency", + "Type" -> "Real", + "Stored" -> True, + "Searchable" -> False, + "Tokenized" -> False, + "BulkRetrievalOptimized" -> True, + "Weight" -> 1 + |>, + <| + "Name" -> "Title", + "Type" -> "Title", + "Stored" -> True, + "Weight" -> 2, + "Tokenized" -> True, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "NormalizedTitle", + "Type" -> "Text", + "Tokenized" -> False, + "LengthWeighted" -> False, + "Stored" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "NotebookPackage", + "Type" -> "Text", + "Stored" -> True, + "Searchable" -> False, + "Tokenized" -> False, + "BulkRetrievalOptimized" -> True, + "Weight" -> 1, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False + |>, + <| + "Name" -> "TokenizedNotebookType", + "Type" -> "Text", + "LengthWeighted" -> False, + "Tokenized" -> True, + "Stored" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "ShortNotations", + "Type" -> "Text", + "Tokenized" -> False, + "LengthWeighted" -> False, + "Stored" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "ReferredBy", + "Type" -> "Text", + "Weight" -> 0.5, + "LengthWeighted" -> False, + "Tokenized" -> True, + "Stored" -> False, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "Text", + "Type" -> "Text", + "Tokenized" -> True, + "Stored" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "TableText", + "Type" -> "Text", + "Tokenized" -> True, + "Stored" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "Abstract", + "Type" -> "Text", + "Weight" -> 1.5, + "Tokenized" -> True, + "Stored" -> False, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "FunctionsSubsection", + "Type" -> "Text", + "Tokenized" -> True, + "Stored" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "LinkedSymbols", + "Type" -> "Text", + "Tokenized" -> True, + "Stored" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "MathCaption", + "Type" -> "Text", + "Tokenized" -> True, + "Stored" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |>, + <| + "Name" -> "Caption", + "Type" -> "Text", + "Tokenized" -> True, + "Stored" -> False, + "Weight" -> 1, + "Searchable" -> True, + "Language" -> "English", + "IgnoreCase" -> True, + "StemmingMethod" -> Automatic, + "CamelCaseMatching" -> True, + "DeleteStopWords" -> True, + "StoreTermVectors" -> False, + "BulkRetrievalOptimized" -> False + |> +} \ No newline at end of file diff --git a/packages/X/Documentation/English/TextSearchIndex/indexMetadata.wl b/packages/X/Documentation/English/TextSearchIndex/indexMetadata.wl new file mode 100644 index 0000000000000000000000000000000000000000..d26b5707ced075d8a21b4b9471d55b5ca6eb65f0 --- /dev/null +++ b/packages/X/Documentation/English/TextSearchIndex/indexMetadata.wl @@ -0,0 +1,62 @@ +<|"IndexedPaths" -> None, "Driver" -> "Lucene", + "CreationDate" -> DateObject[{2017, 11, 25, 16, 59, + 10.603062`7.778006287326521}, "Instant", "Gregorian", -5.], + "Version" -> 1, "Synonyms" -> None, "Method" -> "BM25", + "Language" -> Automatic, "ContentFieldOptions" -> + <|"Title" -> <|"Stored" -> True, "Weight" -> 2|>, + "ExactTitle" -> <|"Stored" -> True, "Tokenized" -> False, + "LengthWeighted" -> False|>, "NormalizedTitle" -> + <|"Tokenized" -> False, "LengthWeighted" -> False|>, + "PossibleAlternateNames" -> <|"Weight" -> 1.5, "LengthWeighted" -> + False|>, "ShortNotations" -> <|"Tokenized" -> False, + "LengthWeighted" -> False|>, "Synonyms" -> <|"Weight" -> 1.5, + "Stored" -> True, "LengthWeighted" -> False|>, + "Keywords" -> <|"Stored" -> True|>, + "URI" -> <|"Stored" -> True, "Tokenized" -> False, + "LengthWeighted" -> False|>, "SnippetPlaintext" -> + <|"Stored" -> True, "Searchable" -> False, "Tokenized" -> False|>, + "ReferredBy" -> <|"Weight" -> 0.5, "LengthWeighted" -> False|>, + "Description" -> <|"Stored" -> True, "Searchable" -> False, + "Tokenized" -> False|>, "PacletName" -> <|"Stored" -> True, + "Searchable" -> False, "Tokenized" -> False|>, + "Language" -> <|"Stored" -> True, "Searchable" -> False, + "Tokenized" -> False|>, "Usage" -> <|"Weight" -> 1.5|>, + "Abstract" -> <|"Weight" -> 1.5|>, "NotebookType" -> + <|"Stored" -> True, "Tokenized" -> False, "BulkRetrievalOptimized" -> + True, "LengthWeighted" -> False|>, "TokenizedNotebookType" -> + <|"LengthWeighted" -> False|>, "DisplayedCategory" -> + <|"Stored" -> True, "Searchable" -> False, "Tokenized" -> False|>, + "URL" -> <|"Stored" -> True, "Searchable" -> False, + "Tokenized" -> False|>, "Context" -> <|"Stored" -> True, + "Searchable" -> False, "Tokenized" -> False|>, + "SeeAlso" -> <|"LengthWeighted" -> False|>, + "ExampleText" -> <|"Weight" -> 0.05|>, "Frequency" -> + <|"Stored" -> True, "Searchable" -> False, "Tokenized" -> False, + "BulkRetrievalOptimized" -> True|>, "NotebookStatus" -> + <|"Stored" -> True, "Searchable" -> False, "Tokenized" -> False, + "BulkRetrievalOptimized" -> True|>, "NotebookPackage" -> + <|"Stored" -> True, "Searchable" -> False, "Tokenized" -> False, + "BulkRetrievalOptimized" -> True|>, "Dictionary" -> + <|"OmitTermFreqAndPositions" -> True|>|>, "ContentLocationFunction" -> + <|"SnippetSource" -> ("field:SnippetPlaintext" & ), + "ReferenceLocation" -> Function[DocumentationSearch`Private`c, + URL[StringReplace[DocumentationSearch`Private`c["URL"], + "http://reference.wolfram.com/language/" -> + "http://reference.wolframcloud.com/cloudplatform/"]]]|>, + "DocumentWeightingRules" -> + <|"NotebookType" -> {"Symbol" -> 1., "Guide" -> 1., "Root Guide" -> 1., + "Upgrade Information" -> 1., "Format" -> 0.9166666666666666, + "Interpreter" -> 0.9166666666666666, "Method" -> 0.9166666666666666, + "Tutorial" -> 0.8333333333333334, "Overview" -> 0.8333333333333334, + "Device Connection" -> 0.8333333333333334, "Service Connection" -> + 0.8333333333333334, "Character Name" -> 0.75, + "MathLink C Function" -> 0.75, "System Program" -> 0.6666666666666666, + "Program" -> 0.6666666666666666, "File" -> 0.6666666666666666, + "Embedding Format" -> 0.6666666666666666, "Indicator" -> + 0.6666666666666666, "Front End Object" -> 0.5833333333333334, + "Example" -> 0.5, "Menu Item" -> 0.5, "Message" -> 0.5, + "Widget" -> 0.5}, "NotebookStatus" -> {"ObsoleteFlag" -> 1.*^-6, + "AwaitingFutureDesignReviewFlag" -> 0.25, "NewInOldVersion" -> 0.00001, + "None" -> 1.}, "NotebookPackage" -> {"Compatibility" -> 1., + "Package" -> 0.2, "Mathematica" -> 1.}|>, + "DocumentWeightingFunction" -> {"min(max(1+(log10(Frequency)),0.1),1.5)"}|> diff --git 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These \ +identities are:\ +\>", "Text", + CellID->692712690], + +Cell[BoxData[ + FormBox[ + TagBox[ + StyleBox[ + RowBox[{"{", + StyleBox[GridBox[{ + { + RowBox[{ + RowBox[{ + SuperscriptBox[ + RowBox[{"\[CapitalGamma]", "(", "f", ")"}], "\[Mu]\[Nu]\[Rho]"], + SubscriptBox["p", + RowBox[{"1", "\[Nu]"}]]}], "=", "0"}]}, + { + RowBox[{ + RowBox[{ + SuperscriptBox[ + RowBox[{"\[CapitalGamma]", "(", "f", ")"}], "\[Mu]\[Nu]\[Rho]"], + SubscriptBox["p", + RowBox[{"2", "\[Rho]"}]]}], "=", "0"}]} + }], + ShowAutoStyles->True]}], + ShowAutoStyles->False], + #& ], TraditionalForm]], "NumberedEquation", + CellID->536532277] +}, Open ]], + +Cell[TextData[{ + "We can check these by contracting ", + Cell[BoxData[ + FormBox[ + SubsuperscriptBox["p", "1", "\[Nu]"], TraditionalForm]], "InlineMath"], + " and ", + Cell[BoxData[ + FormBox[ + SubsuperscriptBox["p", "2", "\[Rho]"], TraditionalForm]], "InlineMath"], + " into the vertex function." +}], "Text", + CellID->804006176], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Contract ", + Cell[BoxData[ + FormBox[ + SubsuperscriptBox["p", "1", "\[Nu]"], TraditionalForm]], "InlineMath"], + " and ", + Cell[BoxData[ + FormBox[ + SubsuperscriptBox["p", "2", "\[Rho]"], TraditionalForm]], "InlineMath"], + " into the vertex function, and apply the on shell conditions:" +}], "MathCaption", + Deletable->True, + CellID->1078874899], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"(*", + RowBox[{"Index", " ", "\[Nu]"}], "*)"}], + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"Contract", "[", + RowBox[{"computedVertexFunction", " ", + SubscriptBox["p1", "\[Nu]"]}], "]"}], "/.", "onShell"}], "//", + "Simplify"}], "\[IndentingNewLine]", + RowBox[{"(*", + RowBox[{"Index", " ", "\[Rho]"}], "*)"}], " ", + RowBox[{ + RowBox[{ + RowBox[{"Contract", "[", + RowBox[{"computedVertexFunction", " ", + SubscriptBox["p2", "\[Rho]"]}], "]"}], "/.", "onShell"}], "//", + "Simplify"}]}]}]], "Input", + CellLabel->"In[14]:=", + CellID->1445995872], + +Cell[BoxData[ + RowBox[{ + RowBox[{"-", "4"}], " ", "\[ImaginaryI]", " ", "gA", " ", + SuperscriptBox["Q", "2"], " ", + SubscriptBox["\[CurlyEpsilon]", + RowBox[{"\[Mu]", ",", "\[Rho]", ",", + RowBox[{"{", "p1", "}"}], ",", + RowBox[{"{", "p2", "}"}]}]]}]], "Output", + ImageSize->{140, 18}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[14]=", + CellID->866335895], + +Cell[BoxData[ + RowBox[{"4", " ", "\[ImaginaryI]", " ", "gA", " ", + SuperscriptBox["Q", "2"], " ", + SubscriptBox["\[CurlyEpsilon]", + RowBox[{"\[Mu]", ",", "\[Nu]", ",", + RowBox[{"{", "p1", "}"}], ",", + RowBox[{"{", "p2", "}"}]}]]}]], "Output", + ImageSize->{132, 18}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[15]=", + CellID->568260605] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "The Ward identities require these expressions to vanish, so something has \ +gone awry in the computation. Let's parametrize the ", + Cell[BoxData[ + FormBox["Z\[Gamma]\[Gamma]", TraditionalForm]], "InlineMath"], + " vertex function in the following way:" +}], "Text", + Deletable->True, + CellID->276667481], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"i", " ", + SuperscriptBox[ + RowBox[{"\[CapitalGamma]", "(", "f", ")"}], "\[Mu]\[Nu]\[Rho]"]}], " ", + "=", " ", + RowBox[{ + RowBox[{ + SubscriptBox["F", "1"], + SubsuperscriptBox["p", "1", "\[Mu]"], + SubscriptBox["p", + RowBox[{"1", "\[Alpha]"}]], + SubscriptBox["p", + RowBox[{"2", "\[Beta]"}]], + SuperscriptBox["\[Epsilon]", "\[Nu]\[Rho]\[Alpha]\[Beta]"]}], "+", + RowBox[{ + SubscriptBox["F", "2"], + SubsuperscriptBox["p", "2", "\[Mu]"], + SubscriptBox["p", + RowBox[{"1", "\[Alpha]"}]], + SubscriptBox["p", + RowBox[{"2", "\[Beta]"}]], + SuperscriptBox["\[Epsilon]", "\[Nu]\[Rho]\[Alpha]\[Beta]"]}], "+", + RowBox[{ + SubscriptBox["F", "3"], + SubsuperscriptBox["p", "1", "\[Nu]"], + SubscriptBox["p", + RowBox[{"1", "\[Alpha]"}]], + SubscriptBox["p", + RowBox[{"2", "\[Beta]"}]], + SuperscriptBox["\[Epsilon]", "\[Mu]\[Rho]\[Alpha]\[Beta]"]}], "+", + "\[IndentingNewLine]", + RowBox[{ + SubscriptBox["F", "4"], + SubsuperscriptBox["p", "2", "\[Nu]"], + SubscriptBox["p", + RowBox[{"1", "\[Alpha]"}]], + SubscriptBox["p", + RowBox[{"2", "\[Beta]"}]], + SuperscriptBox["\[Epsilon]", "\[Mu]\[Rho]\[Alpha]\[Beta]"]}], "+", + RowBox[{ + SubscriptBox["F", "5"], + SubsuperscriptBox["p", "1", "\[Rho]"], + SubscriptBox["p", + RowBox[{"1", "\[Alpha]"}]], + SubscriptBox["p", + RowBox[{"2", "\[Beta]"}]], + SuperscriptBox["\[Epsilon]", "\[Mu]\[Nu]\[Alpha]\[Beta]"]}], "+", + RowBox[{ + SubscriptBox["F", "6"], + SubsuperscriptBox["p", "2", "\[Rho]"], + SubscriptBox["p", + RowBox[{"1", "\[Alpha]"}]], + SubscriptBox["p", + RowBox[{"2", "\[Beta]"}]], + SuperscriptBox["\[Epsilon]", "\[Mu]\[Nu]\[Alpha]\[Beta]"]}], "+", + RowBox[{ + SubscriptBox["G", "1"], + SubscriptBox["p", + RowBox[{"1", "\[Alpha]"}]], + SuperscriptBox["\[Epsilon]", "\[Mu]\[Nu]\[Rho]\[Alpha]"]}], "+", + RowBox[{ + SubscriptBox["G", "2"], + SubscriptBox["p", + RowBox[{"2", "\[Alpha]"}]], + SuperscriptBox["\[Epsilon]", "\[Mu]\[Nu]\[Rho]\[Alpha]"]}]}]}], + TraditionalForm]], "NumberedEquation", + CellID->1753847449] +}, Open ]], + +Cell["\<\ +To diagnose the problem, it is useful to note the superficial UV degrees of \ +divergence of the varous form factors:\ +\>", "Text", + Deletable->True, + CellID->819122462], + +Cell[BoxData[GridBox[{ + {Cell["Quantity", "TableHeader"], Cell[ + "Superficial degree of divergence", "TableHeader"]}, + {Cell[TextData[{ + Cell[BoxData[ + FormBox[ + SuperscriptBox["\[CapitalGamma]", "\[Mu]\[Nu]\[Rho]"], + TraditionalForm]], "InlineMath"], + " (Full integral)" + }], "TableText", + Deletable->True], Cell["+1 (linearly divergent)", "TableText"]}, + {Cell[TextData[{ + Cell[BoxData[ + FormBox[ + SubscriptBox["F", "1"], TraditionalForm]], "InlineMath"], + "\[LongDash]", + Cell[BoxData[ + FormBox[ + SubscriptBox["F", "6"], TraditionalForm]], "InlineMath"] + }], "TableText", + Deletable->True], Cell["\[Dash]2 (finite)", "TableText"]}, + {Cell[TextData[{ + Cell[BoxData[ + FormBox[ + SubscriptBox["G", "1"], TraditionalForm]], "InlineMath"], + ", ", + Cell[BoxData[ + FormBox[ + SubscriptBox["G", "2"], TraditionalForm]], "InlineMath"] + }], "TableText", + Deletable->True], Cell[" 0 (logarithmically divergent)", "TableText"]} + }]], "DefinitionBox", + CellID->1152923733], + +Cell["Superficial UV degrees of divergence.", "Caption", + CellID->444233650], + +Cell[TextData[{ + "Form factors ", + Cell[BoxData[ + FormBox[ + SubscriptBox["F", "1"], TraditionalForm]], "InlineMath"], + "\[LongDash]", + Cell[BoxData[ + FormBox[ + SubscriptBox["F", "6"], TraditionalForm]], "InlineMath"], + " are UV convergent, so their forms are unambiguous. But form factors ", + Cell[BoxData[ + FormBox[ + SubscriptBox["G", "1"], TraditionalForm]], "InlineMath"], + " and ", + Cell[BoxData[ + FormBox[ + SubscriptBox["G", "2"], TraditionalForm]], "InlineMath"], + " are superficially logarithmically divergent. So, their precise forms \ +depend on the UV regulator. Within dimensional regularization they will \ +especially depend on how ", + Cell[BoxData[ + FormBox[ + SubscriptBox["\[Gamma]", "5"], TraditionalForm]], "InlineMath"], + " is treated. Since ", + StyleBox["Package", + FontSlant->"Italic"], + "-X's ", + Cell[BoxData[ + ButtonBox["\[Gamma]5", + BaseStyle->"Link", + ButtonData->"paclet:X/ref/DiracG5"]], "InlineFormula", + FontFamily->FEPrivate`If[ + FEPrivate`Or[ + FEPrivate`SameQ[FEPrivate`$ProductVersion, "11.1"], + FEPrivate`SameQ[FEPrivate`$ProductVersion, "11.2"]], "Source Sans Pro", + Inherited]], + " anticommutes with all other gamma matrices, which is techincally \ +inconsistent within dimensional regularization, we can expect that ", + Cell[BoxData[ + FormBox[ + SubscriptBox["G", "1"], TraditionalForm]], "InlineMath"], + " and ", + Cell[BoxData[ + FormBox[ + SubscriptBox["G", "2"], TraditionalForm]], "InlineMath"], + " are incorrect, leading to the violations of Ward identities." +}], "Text", + CellID->1543004124], + +Cell[TextData[{ + "Next, we will apply Adler's method to correct the form factors ", + Cell[BoxData[ + FormBox[ + SubscriptBox["G", "1"], TraditionalForm]], "InlineMath"], + " and ", + Cell[BoxData[ + FormBox[ + SubscriptBox["G", "2"], TraditionalForm]], "InlineMath"], + ". We will determine them in terms of the unambiguous form factors ", + Cell[BoxData[ + FormBox[ + SubscriptBox["F", "1"], TraditionalForm]], "InlineMath"], + "\[LongDash]", + Cell[BoxData[ + FormBox[ + SubscriptBox["F", "6"], TraditionalForm]], "InlineMath"], + " by requiring that the QED Ward identities be satisfied at the \[Nu] and \ +\[Rho] vertices." +}], "Text", + CellID->1340610167], + +Cell[TextData[{ + "Let's start by storing the form factors ", + Cell[BoxData[ + FormBox[ + SubscriptBox["F", "1"], TraditionalForm]], "InlineMath"], + "\[LongDash]", + Cell[BoxData[ + FormBox[ + SubscriptBox["F", "6"], TraditionalForm]], "InlineMath"], + ", by extracting the coefficients of the multiplying tensors. 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Since the tensor algebraic \ +capabilities of FeynCalc are more comprehensive than those of Package-X, it \ +is expedient to carry out the bulk of your calculations with FeynCalc, and \ +only use Package-X's OneLoop.m file as a library of analytic one-loop \ +integrals. The add-on FeynHelpers to FeynCalc provides this interface. This \ +tutorial illustrates how you can analytically evaluate one loop integrals in \ +FeynCalc using FeynHelpers. After installing FeynCalc 9.2 or later together \ +with FeynHelpers 1.1, initialize them from a fresh kernel: Restart kernel to \ +start a new Mathematica session. 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"language" -> "en", "paclet" -> + "Package-X", "status" -> "None", "summary" -> + "A direct consequence of unitarity of the relativsitic S-matrix is the \ +optical theorem which relates the imaginary part of the forward (t=0) elastic \ +scattering amplitude to the total cross section. Since the cross section \ +itself depends on the square of the scattering amplitude the optical theorem \ +provides a relationship that is nonlinear in the coupling \ +constant\[LongDash]frequently the perturbation parameter. Therefore, the \ +optical theorem allows us to calculate cross sections at lower orders in \ +pertubation theory using information from the higher order amplitude with the \ +phase space integration already done.", "synonyms" -> {}, "title" -> + "Evaluation of e^+e^-\[Rule]\[Gamma]\[Gamma] Cross Section by The Optical \ +Theorem", "titlemodifier" -> "", "windowtitle" -> + "Evaluation of e^+e^-\[Rule]\[Gamma]\[Gamma] Cross Section by The Optical \ +Theorem", "type" -> "Tutorial", "uri" -> + "X/tutorial/PairAnnihilationUnitarity"}, "SearchTextTranslated" -> ""}, +FrontEndVersion -> "6.0", +StyleDefinitions->Notebook[{ + Cell[ + StyleData[ + StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], + Cell[ + StyleData["Input"], CellContext -> Notebook], + Cell[ + StyleData["Output"], CellContext -> Notebook], + Cell[ + StyleData["TutorialMoreAboutSection"], + CellGroupingRules -> {"SectionGrouping", 30}], + Cell[ + StyleData["RelatedTutorialsSection"], + CellGroupingRules -> {"SectionGrouping", 30}], + Cell[ + StyleData["TutorialRelatedLinksSection"], + CellGroupingRules -> {"SectionGrouping", 30}]}, Visible -> False, + FrontEndVersion -> "6.0", + StyleDefinitions -> "Default.nb"] +] + diff --git a/packages/X/Documentation/English/Tutorials/ScatteringLightByLight.nb b/packages/X/Documentation/English/Tutorials/ScatteringLightByLight.nb new file mode 100644 index 0000000000000000000000000000000000000000..151cc8955912d0e52d4b049b8a71542fdb0b471b --- /dev/null +++ b/packages/X/Documentation/English/Tutorials/ScatteringLightByLight.nb @@ -0,0 +1,7090 @@ +Notebook[{ +Cell[BoxData[GridBox[{ + {Cell["PACKAGE-X TUTORIAL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox["\<\"Related Tutorials \[RightGuillemet]\"\>", + StripOnInput-> + False], {"\<\"Bringing the Arguments of D functions to Canonical \ +Form\"\>":>Documentation`HelpLookup["paclet:X/tutorial/ArgumentsOfScalarD"]}, + Appearance->None, + MenuAppearance->Automatic]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox["\<\"More About \[RightGuillemet]\"\>", + StripOnInput->False], {"\<\"Package-X\"\>":>Documentation`HelpLookup[ + "paclet:X/guide/PackageX"]}, + Appearance->None, + MenuAppearance->Automatic]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox["\<\"URL \[RightGuillemet]\"\>", + StripOnInput->False], {"\<\"X/tutorial/LightByLight\"\>":> + None, "\<\"Copy Mathematica url\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["X/tutorial/LightByLight"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web url\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/mathematica/X/tutorial/\ +LightByLight.html"], StandardForm]], "Input", TextClipboardType -> + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web url\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + "http://reference.wolfram.com/mathematica/", + "X/tutorial/LightByLight", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} + }]], "AnchorBarGrid", + CellID->1], + +Cell[CellGroupData[{ + +Cell["The Scattering of Light By Light", "Title", + CellID->509267359], + +Cell[TextData[{ + "This tutorial will illustrate a few strategies you can employ to streamline \ +complex calculations with ", + StyleBox["Package", + FontSlant->"Italic"], + "-X by using the scattering of light by light in quantum electrodynamics as \ +an example. 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strategies you can employ to \ +streamline complex calculations with Package-X by using the scattering of \ +light by light in quantum electrodynamics as an example. We will aim to \ +calculate the scattering amplitude and differential cross section. In certain \ +kinematic limits, compact analytic expressions exist and can be quickly \ +obtained. Otherwise, the general result with full kinematic dependence is \ +extremely complicated, and can take a long time to calculate. But with clever \ +strategies it can be obtained in a reasonable amount of time, and can even be \ +numerically evaluated. We will also save the final result so it can be \ +reloaded upon restarting Mathematica. At leading order, the Feynman diagrams \ +are: GridBox[{{StyleBox[\"s-channel\", TR], StyleBox[\"t-channel\", TR], \ +StyleBox[\"u-channel\", TR]}, {", "synonyms" -> {}, "title" -> + "The Scattering of Light By Light", "titlemodifier" -> "", "windowtitle" -> + "The Scattering of Light By Light", "type" -> "Tutorial", "uri" -> + "X/tutorial/LightByLight"}, "SearchTextTranslated" -> ""}, +FrontEndVersion -> "6.0", +StyleDefinitions->Notebook[{ + Cell[ + StyleData[ + StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], + Cell[ + StyleData["Input"], CellContext -> Notebook], + Cell[ + StyleData["Output"], CellContext -> Notebook], + Cell[ + StyleData["TutorialMoreAboutSection"], + CellGroupingRules -> {"SectionGrouping", 30}], + Cell[ + StyleData["RelatedTutorialsSection"], + CellGroupingRules -> {"SectionGrouping", 30}], + Cell[ + StyleData["TutorialRelatedLinksSection"], + CellGroupingRules -> {"SectionGrouping", 30}]}, Visible -> False, + FrontEndVersion -> "6.0", + StyleDefinitions -> "Default.nb"] +] + diff --git a/packages/X/Kernel/init.m b/packages/X/Kernel/init.m new file mode 100644 index 0000000000000000000000000000000000000000..f95dc3387d1b96378302c7139cc2f55856138b24 --- /dev/null +++ b/packages/X/Kernel/init.m @@ -0,0 +1,32 @@ +(* ::Package:: *) + +(* Mathematica Init File *) +System`Dump`fixmessagestring[System`Dump`s_] := ToString@InputForm@System`Dump`s; + +If[MemberQ[Contexts[], "X`"], + If[$KernelID==0, + If[$Notebooks, + Print[ToString[Row[{"Package-X v2.1.1 already initialized\nFor more information, see the ", Hyperlink["guide", "paclet:X/guide/PackageX"]}],StandardForm]], + Print["Package-X v2.1.1 already initialized"] + ] + ], + + BeginPackage["X`"]; + Get[FileNameJoin[{DirectoryName[$InputFileName,2], "Common.m"}]]; + Get[FileNameJoin[{DirectoryName[$InputFileName,2], "Lorentz.m"}]]; + Get[FileNameJoin[{DirectoryName[$InputFileName,2], "Dirac.m"}]]; + Get[FileNameJoin[{DirectoryName[$InputFileName,2], "OneLoop.m"}]]; + + EndPackage[]; + + If[$KernelID==0, + If[$Notebooks, + If[$VersionNumber<10.1, Print[ToString[Row[{"Attention: Support for Mathematica earlier than version 10.1 will be dropped in the near future. Please upgrade your copy of ", Hyperlink["Mathematica", "http://www.wolfram.com/mathematica/"]}],StandardForm]]]; + Print[ToString[Row[{"Package-X v2.1.1, by Hiren H. Patel\nFor more information, see the ", Hyperlink["guide", "paclet:X/guide/PackageX"]}],StandardForm]], + + If[$VersionNumber<10.1, Print["Attention: Support for Mathematica earlier than version 10.1 will be dropped in the near future. Please upgrade your copy of Mathematica"]]; + Print["Package-X v2.1.1, by Hiren H. 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Patel", + Extensions -> + { + {"Kernel", Root -> ".", Context -> + {"X`"} + }, + {"Documentation", Language -> "English", MainPage -> "Guides/PackageX"} + } +] + + diff --git a/packages/colliderfourvec.wl b/packages/colliderfourvec.wl new file mode 100644 index 0000000000000000000000000000000000000000..a519d0e4574939c4e438924b8a1edd7fbed87cc5 --- /dev/null +++ b/packages/colliderfourvec.wl @@ -0,0 +1,73 @@ +(* ::Package:: *) + +BeginPackage["colliderfourvec`"] + + + Print["colliderfourvec by J.G. Reyes v1. May 2019"] + + ek1::usage = "ind. polarization vector" + ek2::usage = "ind. polarization vector" + ek3::usage = "ind. polarization vector and longitudinal helicity eigenvector" + ek1c::usage = "ek1 in collider coordinates" + ek2c::usage = "ek2 in collider coordinates" + ek3c::usage = "ek3 in collider coordinates" + ekT::usage = "transverse helicity eigenvector" + ekTstar::usage = "c.c. transverse helicity eigenvector" + ekTc::usage = "ekT in collider coordinates" + ekTcstar::usage = "ekTstar in collider coordinates" + Epol::usage = "four vector using ekT/ekTstar/ek3" + Epolstar::usage = "four vector c.c. using ekT/ekTstar/ek3" + Epolc::usage = "Epol in collider coordinates" + Epolcstar::usage = "Epolstar in collider coordinates" + gmn::usage = "metric tensor" + Gmn::usage = "metric tensor elements" + MyPair::usage = "contracts two four vectors" + Cov4::usage = "covariant form for a four vector" + vec4::usage = "four vector" + vec4M::usage = "massive four vector" + vec4c::usage = "four vector in collider coordinates" + vec4Mc::usage = "massive four vector in collider coordinates" + Begin["Private`"] + (*pT = p*Sin[\[Theta]]; + EnT = En*Sin[\[Theta]]; + mT = Sqrt[m^2+px^2+py^2] + y = (1/2)*((E+ppara)/(E-ppara)) + En = (1/2)*(e^y)*(m^2+p^2perp) + Eta = -log[Tan[\[Theta]/2]]; + \[Theta]=2ArcTan[E^\[Eta]];*) + + + ek1[k_,\[Theta]_,\[Phi]_]:= (1/(k *(k Sin[\[Theta]])))*{0,k^2 Sin[\[Theta]]Cos[\[Phi]]Cos[\[Theta]],k^2 Sin[\[Theta]]Sin[\[Phi]]Cos[\[Theta]], -k^2 Sin[\[Theta]]^2}; + ek2[k_,\[Theta]_,\[Phi]_]:= (1/(k Sin[\[Theta]]))*{0,-k Sin[\[Theta]]Sin[\[Phi]],k Sin[\[Theta]]Cos[\[Phi]],0}; + ek3[m_,k_,\[Theta]_,\[Phi]_]:= (Sqrt[k^2+m^2]/(m*k))*{k^2/Sqrt[k^2+m^2],k Sin[\[Theta]] Cos[\[Phi]],k Sin[\[Theta]] Sin[\[Phi]],k Cos[\[Theta]]}; + + ek1c[pT_,\[Eta]_,\[Phi]_]:=(1/(pT Cosh[\[Eta]] *pT)){0,pT^2 Cos[\[Phi]]Sinh[\[Eta]],pT^2 Sin[\[Phi]]Sinh[\[Eta]], -pT^2}; + ek2c[pT_,\[Eta]_,\[Phi]_]:=(1/pT){0,-pT Sin[\[Phi]],pT Cos[\[Phi]],0}; + ek3c[m_,pT_,\[Eta]_,\[Phi]_]:=(Sqrt[pT^2+(pT*Sinh[\[Eta]])^2+m^2]/(m*(pT Cosh[\[Eta]])))*{(pT Cosh[\[Eta]])^2/Sqrt[pT^2+(pT*Sinh[\[Eta]])^2+m^2],pT Cos[\[Phi]],pT Sin[\[Phi]],pT Sinh[\[Eta]]}; + + ekT[l_,k_,\[Theta]_,\[Phi]_]:=Sqrt[1/2]*(-l*ek1[k,\[Theta],\[Phi]]-I*ek2[k,\[Theta],\[Phi]]); + ekTstar[l_,k_,\[Theta]_,\[Phi]_]:= Sqrt[1/2]*(-l*ek1[k,\[Theta],\[Phi]]+I*ek2[k,\[Theta],\[Phi]]); + + ekTc[l_,pT_,\[Eta]_,\[Phi]_]:=Sqrt[1/2]*(-l*ek1c[pT,\[Eta],\[Phi]]-I*ek2c[pT,\[Eta],\[Phi]]); + ekTcstar[l_,pT_,\[Eta]_,\[Phi]_]:= Sqrt[1/2]*(-l*ek1c[pT,\[Eta],\[Phi]]+I*ek2c[pT,\[Eta],\[Phi]]); + + Epol[m_,k_,\[Theta]_,\[Phi]_,l_]:=Module[{m1=m,k1=k,t1=\[Theta],p1=\[Phi],l1=l},Switch[l1,0,ek3[m1,k1,t1,p1],1,ekT[1,k1,t1,p1],-1,ekT[-1,k1,t1,p1], _,Message["Polarization Does not exist"]]]; + Epolstar[m_,k_,\[Theta]_,\[Phi]_,l_]:=Module[{m1=m,k1=k,t1=\[Theta],p1=\[Phi],l1=l},Switch[l1,0,ek3[m1,k1,t1,p1],1,ekTstar[1,k1,t1,p1],-1,ekTstar[-1,k1,t1,p1], _,Message["Polarization Does not exist"]]]; + + Epolc[m_,pT_,\[Eta]_,\[Phi]_,l_]:=Module[{m1=m,pT1=pT,e1=\[Eta],p1=\[Phi],l1=l},Switch[l1,0,ek3c[m1,pT1,e1,p1],1,ekTc[1,pT1,e1,p1],-1,ekTc[-1,pT1,e1,p1], _,Message["Polarization Does not exist"]]]; + Epolcstar[m_,pT_,\[Eta]_,\[Phi]_,l_]:=Module[{m1=m,pT1=pT,e1=\[Eta],p1=\[Phi],l1=l},Switch[l1,0,ek3c[m1,pT1,e1,p1],1,ekTcstar[1,pT1,e1,p1],-1,ekTcstar[-1,pT1,e1,p1], _,Message["Polarization Does not exist"]]]; + + gmn={{1,0,0,0},{0,-1,0,0},{0,0,-1,0},{0,0,0,-1}}; + Gmn[m_,n_]:=Module[{m1=m,n1=n},gmn[[m1,n1]]]; + MyPair[k1_,k2_]:=Module[{p1=k1,p2=k2,x1,x2,x},x1=p1[[All]];x2=p2[[All]];x=Simplify[Sum[Gmn[i,i]x1[[i]] x2[[i]],{i,1,4}]];x]; + Cov4[p1_]:=Module[{k1=p1,x=p1},Do[x[[n]]=Gmn[n,n]k1[[n]],{n,1,4}];x]; + vec4[k_,\[Theta]_,\[Phi]_]:=Module[{},{k,k Sin[\[Theta]] Cos[\[Phi]],k Sin[\[Theta]] Sin[\[Phi]],k Cos[\[Theta]]}]; + vec4M[m_,k_,\[Theta]_,\[Phi]_]:=Module[{},{Sqrt[k^2 + m^2],k Sin[\[Theta]] Cos[\[Phi]],k Sin[\[Theta]] Sin[\[Phi]],k Cos[\[Theta]]}]; + vec4c[pT_,\[Eta]_,\[Phi]_]:=Module[{},{pT Cosh[\[Eta]],pT Cos[\[Phi]],pT Sin[\[Phi]],pT Sinh[\[Eta]]}]; + vec4Mc[m_,pT_,\[Eta]_,\[Phi]_]:=Module[{},{Sqrt[m^2+(pT Cosh[\[Eta]])^2],pT Cos[\[Phi]],pT Sin[\[Phi]],pT Sinh[\[Eta]]}]; + + + +End[] + +EndPackage[] diff --git a/packages/helicityvec.wl b/packages/helicityvec.wl new file mode 100644 index 0000000000000000000000000000000000000000..0dddd7555eaab2b11ed97c3667ade99658eebca6 --- /dev/null +++ b/packages/helicityvec.wl @@ -0,0 +1,89 @@ +(* ::Package:: *) + +BeginPackage["helicityvec`"] + + + Print["helicityvec by J.G. Reyes v1. August 2019"] + ek1Euc::usage = "ind. polarization vector in Euclidean coordinates" + ek2Euc::usage = "ind. polarization vector in Euclidean coordinates" + ek3Euc::usage = "ind. polarization vector and longitudinal helicity eigenvector in Euclidean coordinates" + ek1::usage = "ind. polarization vector" + ek2::usage = "ind. polarization vector" + ek3::usage = "ind. polarization vector and longitudinal helicity eigenvector" + ek1c::usage = "ek1 in collider coordinates" + ek2c::usage = "ek2 in collider coordinates" + ek3c::usage = "ek3 in collider coordinates" + ekT::usage = "transverse helicity eigenvector" + ekTstar::usage = "c.c. transverse helicity eigenvector" + ekTEuc::usage = "transverse helicity eigenvector in Euclidean coordinates" + ekTstarEuc::usage = "c.c. transverse helicity eigenvector in Euclidean coordinates" + ekTc::usage = "ekT in collider coordinates" + ekTcstar::usage = "ekTstar in collider coordinates" + Epol::usage = "four vector using ekT/ekTstar/ek3" + Epolstar::usage = "four vector c.c. using ekT/ekTstar/ek3" + Epolc::usage = "Epol in collider coordinates" + Epolcstar::usage = "Epolstar in collider coordinates" + EpolEuc::usage = "Epol in Euclidean coordinates" + EpolstarEuc::usage = "Epolstar in Euclidean coordinates" + gmn::usage = "metric tensor" + Gmn::usage = "metric tensor elements" + MyPair::usage = "contracts two four vectors" + Cov4::usage = "covariant form for a four vector" + vec4::usage = "four vector" + vec4M::usage = "massive four vector" + vec4c::usage = "four vector in collider coordinates" + vec4Mc::usage = "massive four vector in collider coordinates" + Begin["Private`"] + (*pT = p*Sin[\[Theta]]; + EnT = En*Sin[\[Theta]]; + mT = Sqrt[m^2+px^2+py^2] + y = (1/2)*((E+ppara)/(E-ppara)) + En = (1/2)*(e^y)*(m^2+p^2perp) + Eta = -log[Tan[\[Theta]/2]]; + \[Theta]=2ArcTan[E^\[Eta]];*) + + + ek1Euc[kx_,ky_,kz_]:= Module[{magk=Sqrt[kx^2+ky^2+kz^2],kT=Sqrt[kx^2+ky^2]},(1/(magk *(kT)))*{0,kx*kz,ky*kz,-kT^2}]; + ek2Euc[kx_,ky_,kz_]:= Module[{kT=Sqrt[kx^2+ky^2]},(1/kT)*{0,-ky,kx,0}]; + ek3Euc[m_,kx_,ky_,kz_]:= Module[{E=Sqrt[m^2+kx^2+ky^2+kz^2],magk=Sqrt[kx^2+ky^2]},(E/(m*magk))*{magk^2/E,kx,ky,kz}]; + + ek1[k_,\[Theta]_,\[Phi]_]:= (1/(k *(k Sin[\[Theta]])))*{0,k^2 Sin[\[Theta]]Cos[\[Phi]]Cos[\[Theta]],k^2 Sin[\[Theta]]Sin[\[Phi]]Cos[\[Theta]], -k^2 Sin[\[Theta]]^2}; + ek2[k_,\[Theta]_,\[Phi]_]:= (1/(k Sin[\[Theta]]))*{0,-k Sin[\[Theta]]Sin[\[Phi]],k Sin[\[Theta]]Cos[\[Phi]],0}; + ek3[m_,k_,\[Theta]_,\[Phi]_]:= (Sqrt[k^2+m^2]/(m*k))*{k^2/Sqrt[k^2+m^2],k Sin[\[Theta]] Cos[\[Phi]],k Sin[\[Theta]] Sin[\[Phi]],k Cos[\[Theta]]}; + + ek1c[pT_,\[Eta]_,\[Phi]_]:=(1/(pT Cosh[\[Eta]] *pT)){0,pT^2 Cos[\[Phi]]Sinh[\[Eta]],pT^2 Sin[\[Phi]]Sinh[\[Eta]], -pT^2}; + ek2c[pT_,\[Eta]_,\[Phi]_]:=(1/pT){0,-pT Sin[\[Phi]],pT Cos[\[Phi]],0}; + ek3c[m_,pT_,\[Eta]_,\[Phi]_]:=(Sqrt[pT^2+(pT*Sinh[\[Eta]])^2+m^2]/(m*(pT Cosh[\[Eta]])))*{(pT Cosh[\[Eta]])^2/Sqrt[pT^2+(pT*Sinh[\[Eta]])^2+m^2],pT Cos[\[Phi]],pT Sin[\[Phi]],pT Sinh[\[Eta]]}; + + ekT[l_,k_,\[Theta]_,\[Phi]_]:=Sqrt[1/2]*(-l*ek1[k,\[Theta],\[Phi]]-I*ek2[k,\[Theta],\[Phi]]); + ekTstar[l_,k_,\[Theta]_,\[Phi]_]:= Sqrt[1/2]*(-l*ek1[k,\[Theta],\[Phi]]+I*ek2[k,\[Theta],\[Phi]]); + + ekTc[l_,pT_,\[Eta]_,\[Phi]_]:=Sqrt[1/2]*(-l*ek1c[pT,\[Eta],\[Phi]]-I*ek2c[pT,\[Eta],\[Phi]]); + ekTcstar[l_,pT_,\[Eta]_,\[Phi]_]:= Sqrt[1/2]*(-l*ek1c[pT,\[Eta],\[Phi]]+I*ek2c[pT,\[Eta],\[Phi]]); + + ekTEuc[l_,kx_,ky_,kz_]:=Sqrt[1/2]*(-l*ek1Euc[kx,ky,kz]-I*ek2Euc[kx,ky,kz]); + ekTstarEuc[l_,kx_,ky_,kz_]:= Sqrt[1/2]*(-l*ek1Euc[kx,ky,kz]+I*ek2Euc[kx,ky,kz]); + + Epol[m_,k_,\[Theta]_,\[Phi]_,l_]:=Module[{m1=m,k1=k,t1=\[Theta],p1=\[Phi],l1=l},Switch[l1,0,ek3[m1,k1,t1,p1],1,ekT[1,k1,t1,p1],-1,ekT[-1,k1,t1,p1], _,Message["Polarization Does not exist"]]]; + Epolstar[m_,k_,\[Theta]_,\[Phi]_,l_]:=Module[{m1=m,k1=k,t1=\[Theta],p1=\[Phi],l1=l},Switch[l1,0,ek3[m1,k1,t1,p1],1,ekTstar[1,k1,t1,p1],-1,ekTstar[-1,k1,t1,p1], _,Message["Polarization Does not exist"]]]; + + EpolEuc[m_,kx_,ky_,kz_,l_]:=Module[{M=m,kX=kx,kY=ky,kZ=kz,l1=l},Switch[l1,0,ek3Euc[M,kX,kY,kZ],1,ekTEuc[1,kX,kY,kZ],-1,ekTEuc[-1,kX,kY,kZ], _,Message["Polarization Does not exist"]]]; + EpolstarEuc[m_,kx_,ky_,kz_,l_]:=Module[{M=m,kX=kx,kY=ky,kZ=kz,l1=l},Switch[l1,0,ek3Euc[M,kX,kY,kZ],1,ekTstarEuc[1,kX,kY,kZ],-1,ekTstarEuc[-1,kX,kY,kZ], _,Message["Polarization Does not exist"]]]; + + Epolc[m_,pT_,\[Eta]_,\[Phi]_,l_]:=Module[{m1=m,pT1=pT,e1=\[Eta],p1=\[Phi],l1=l},Switch[l1,0,ek3c[m1,pT1,e1,p1],1,ekTc[1,pT1,e1,p1],-1,ekTc[-1,pT1,e1,p1], _,Message["Polarization Does not exist"]]]; + Epolcstar[m_,pT_,\[Eta]_,\[Phi]_,l_]:=Module[{m1=m,pT1=pT,e1=\[Eta],p1=\[Phi],l1=l},Switch[l1,0,ek3c[m1,pT1,e1,p1],1,ekTcstar[1,pT1,e1,p1],-1,ekTcstar[-1,pT1,e1,p1], _,Message["Polarization Does not exist"]]]; + + gmn={{1,0,0,0},{0,-1,0,0},{0,0,-1,0},{0,0,0,-1}}; + Gmn[m_,n_]:=Module[{m1=m,n1=n},gmn[[m1,n1]]]; + MyPair[k1_,k2_]:=Module[{p1=k1,p2=k2,x1,x2,x},x1=p1[[All]];x2=p2[[All]];x=Simplify[Sum[Gmn[i,i]x1[[i]] x2[[i]],{i,1,4}]];x]; + Cov4[p1_]:=Module[{k1=p1,x=p1},Do[x[[n]]=Gmn[n,n]k1[[n]],{n,1,4}];x]; + vec4[k_,\[Theta]_,\[Phi]_]:=Module[{},{k,k Sin[\[Theta]] Cos[\[Phi]],k Sin[\[Theta]] Sin[\[Phi]],k Cos[\[Theta]]}]; + vec4M[m_,k_,\[Theta]_,\[Phi]_]:=Module[{},{Sqrt[k^2 + m^2],k Sin[\[Theta]] Cos[\[Phi]],k Sin[\[Theta]] Sin[\[Phi]],k Cos[\[Theta]]}]; + vec4c[pT_,\[Eta]_,\[Phi]_]:=Module[{},{pT Cosh[\[Eta]],pT Cos[\[Phi]],pT Sin[\[Phi]],pT Sinh[\[Eta]]}]; + vec4Mc[m_,pT_,\[Eta]_,\[Phi]_]:=Module[{},{Sqrt[m^2+(pT Cosh[\[Eta]])^2],pT Cos[\[Phi]],pT Sin[\[Phi]],pT Sinh[\[Eta]]}]; + + + +End[] + +EndPackage[]