Feynman graph generation and propagator mixing, I

Abstract

This paper discusses the algorithmic generation of Feynman graphs for QFT models that have some form of explicit propagator mixing, including some related theoretical background. Primarily, it is shown that an ordinary Feynman graph generator — ie one that is able to deal with models without mixed propagators — can be employed to simulate the former, more general type of graph generation.Most of the discussion occurs in the context of graph models — simplified versions of QFT models, that retain only the combinatorial features of the latter type of models. There is a single graph model, noted M(L), for each Lagrangian density L but, for each graph model M, there are infinitely many L such that M=M(L); hence, below, L¯ is not unique (that is not a critical issue, though, as L¯ is used mainly for explanatory purposes and the claims do not depend on the specific L¯ that may be chosen).The aforementioned simulation relies on the construction of an appropriate graph model M¯ from the original M(L)=M, such that (i) there is L¯ without mixed propagators which satisfies M¯=M(L¯) (ie M¯ is a type-SD⁎ model), (ii) the Feynman graphs for L can be easily obtained from those generated for L¯, and (iii) the symmetry factors computed for the graphs in L¯ need not be corrected (and, if some care is taken, the same applies to their signs).