For each S[n], the algebraic structure of the output of FeynmanDiagrams is thus of the form

where  are the symmetry factors, and  (each one corresponds to a Feynman diagram) are functions of one or two arguments of the form

or

where  is the number of interaction Lagrangians from which this  function is derived, and  identify fields entering the interaction Lagrangian. The first case corresponds to the tree-level terms appearing in  (so no propagators), and where the argument of  is a function of name _NP, representing the normal product of the (unpaired) fields ; each of which represents an external leg of the corresponding Feynman diagram. In the second case, the second argument of  is a list of lists where each internal list  represents a pairing of two fields (a propagator) and so to a connected line in the Feynman diagram. For the external legs and connected lines, both represented by fields applied at a point, the application point  identifies the vertex where the line joins the Feynman diagram.

Mathematical notation: When the Physics package is loaded in the Standard Graphical User Interface, the _NP function is displayed using textbook notation; for example,  is displayed as ::, and  is displayed as the product of the time ordered normal product _NP with the list representing the propagator. In addition, by entering Physics[Setup](mathematicalnotation = true), or by using the Options dialog (go to Tools -> Options, select the Display tab, and set the Typesetting level dropdown to extended), you can see anticommutative and noncommutative variables displayed in different colors, and more.

Given an interaction Lagrangian, by default FeynmanDiagrams will consider a field of the problem any function of spacetime variables or function name that has been set to represent a quantum operator by the Setup command. You can override that behavior with the optional argument fields = ..., where the right-hand side is a function, the name of a function field, or a set or list of them.

To represent spinor fields, use anticommutative functions. For that purpose, you can set an anticommutative prefix, or simply load the advanced setup of Physics; both of these are done by using the Setup command. To represent the Dirac-conjugate of a spinor field, you can either use the Dagger command together with an anticommutative function, or just use one other anticommutative function.

The summation convention for spacetime, gauge, or spinor repeated indices in products entering the interaction Lagrangian is automatically used by FeynmanDiagrams, so repeated indices of the respective kinds are automatically generated when expanding the time-order products of interaction Lagrangians.

When matrix multiplication enters the interaction Lagrangian, the expression must be entered with the matrix indices explicitly defined. For example, for an interaction Lagrangian in a spinor electrodynamics theory involving Dirac matrices as in , where  and  represent a spinor field and its conjugate, use .

The optional argument numberoflegs = ..., where the right-hand side is an integer between 2 and 9 or a set of them, is used to filter the output of FeynmanDiagrams to include only as many unpaired fields in normal products (the _NP(...) first argument of the returned  functions) as the indicated . Recall that these unpaired fields represent external legs in the corresponding Feynman diagrams. The current implementation computes with up to nine external legs.

The optional argument numberofloops = ..., where the right-hand side is an integer between 0 and 3 or a set of them, is used to filter the output of FeynmanDiagrams to include only as many couples of paired fields (lists in the second argument of the returned ) as the ones that can be included to form the indicated numberofloops in the corresponding Feynman diagrams. The current implementation computes with up to three loops, and the tree-level graphs correspond to numberofloops = 0.

The optional argument normalproducts = ..., where the right-hand side is an ordered list of fields (or field names), is used to filter the output of FeynmanDiagrams to return only the terms entering  having exactly those external legs; that is, having exactly the indicated normal products. Since in this implementation the number of external legs cannot be greater than 9, at most nine fields can be indicated in the arguments of _NP functions on the right-hand side of this option.

The optional argument excludepropagators = ..., where the right-hand side is either a list of two fields or a set or list of these lists, is used to filter out from the output of FeynmanDiagrams all those  functions containing these propagators.

This optional argument also accepts as its right-hand side the keywords cross or free, so that all  functions containing cross propagators (pairings  with ), or free propagators (pairings  with ), respectively, are filtered out from the output of FeynmanDiagrams.

Note: FeynmanDiagrams does not compute terms involving propagators of two equal anticomutative fields taken at different points (vertices). Thus, for example, if  is defined as an anticommutative field, then the output will not contain terms with a propagator .

When using the field, normalproducts, or excludepropagators options, the fields entering the right-hand sides can be referenced by just their names, or also with their functionality; this can be used, for example, to filter out the propagator  only, and not all propagators of the form , which would include as well , and .