How to derive Feynman diagrams for finite-dimensional integrals directly from the BV formalism

Details How to derive Feynman diagrams for finite-dimensional integrals directly from the BV formalism How to derive Feynman diagrams for finite-dimensional integrals directly from the BV formalism

2012-02-07

arxiv.org/abs/1202.1554v1

Physics

Mathematical Physics

8 pages + bibliography, figures drawn in TikZ

Scientific paper

The Batalin-Vilkovisky formalism in quantum field theory was originally invented to avoid the difficult problem of finding diagrammatic descriptions of oscillating integrals with degenerate critical points. But since then, BV algebras have become interesting objects of study in their own right, and mathematicians sometimes have good understanding of the homological aspects of the story without any access to the diagrammatics. In this note we reverse the usual direction of argument: we begin by asking for an explicit calculation of the homology of a BV algebra, and from it derive Wick's Theorem and the other Feynman rules for finite-dimensional integrals.

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