(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 12.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 101172, 2840] NotebookOptionsPosition[ 93268, 2710] NotebookOutlinePosition[ 93604, 2725] CellTagsIndexPosition[ 93561, 2722] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Vacuum Generating Functional for Scalar Fields", "Subsection", CellChangeTimes->{{3.7851430748465767`*^9, 3.785143094364641*^9}},ExpressionUUID->"39853f73-d0b7-4e85-a4e3-\ 07215ceb2294"], Cell["\<\ This is a simple Mathematica Notebook that develops a routine to generate \ scalar Feynman diagrams. It is not very sophisticated and of course one can do a lot better but it is fairly transparent. 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One with combinatorial factor 4/8 = 1/2 is the one \ loop correction. The other DF[2,1] x DF[3,3]^2 is the Feynman propagator\n\ from ", Cell[BoxData[ FormBox[ SubscriptBox["x", "1"], TraditionalForm]], FormatType->"TraditionalForm",ExpressionUUID-> "b4fced57-b730-4093-afdf-acd00e32df69"], " to ", Cell[BoxData[ FormBox[ SubscriptBox["x", "2"], TraditionalForm]], FormatType->"TraditionalForm",ExpressionUUID-> "e5f7972b-e06f-4f1b-b883-c9f2b7f12cde"], " multiplied by a vacuum bubble." }], "Text", CellChangeTimes->{{3.785085296015551*^9, 3.785085439392351*^9}},ExpressionUUID->"347579fe-2a9a-49e0-b245-\ b4473390029b"], Cell["\<\ Now we pack all of these commands into a couple of Modules. The first is \ called DF and simply exists to exploit the fact that the scalar propagator is symmetric between the two ends of the lines; it makes the output easier to \ simplify (but of course for more complicated field you can\[CloseCurlyQuote]t \ necessarily do this). 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Any term with ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["D", "F"], "[", RowBox[{"5", ",", "5"}], "]"}], " "}], TraditionalForm]], FormatType->"TraditionalForm",ExpressionUUID-> "6b75a96e-75f4-49f0-896f-244a989e51d9"], " contains a loop so must be disconnected. 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