nLab
Feynman transform

Overview

The Feynman transform is an operation on the category of twisted modular operads. It gives a way to parametrize various versions of the Kontsevich’s graph complex, by various modular operads. Every modular operad is in particular cyclic (some say “symplectic”). The Feynman transform, up to a shift, reduces to the cobar operad? of the underlying cyclic operad.

The name “Feynman transform” is due to Getzler and Kapranov.

Literature

• Ezra Getzler, Mikhail Kapranov, Modular operads, Compositio Math. 110 (1998), no. 1, 65–126, doi, arXiv:dg-ga/9408003, MR99f:18009
• Serguei Barannikov, Modular operads and Batalin-Vilkovisky geometry, Int. Math. Res. Not. IMRN 2007, no. 19, Art. ID rnm075, 31 pp. arxiv/0912.5484
• André Joyal, Joachim Kock, Feynman graphs, and nerve theorem for compact symmetric multicategories, proceedings “Quantum Physics and Logic VI”, arxiv/0908.2675
• Joseph Chuang, Andrey Lazarev, Dual Feynman transform for modular operads, arxiv/0704.2561
• Martin Markl, Steve Shnider, Jim Stasheff, Operads in algebra, topology and physics, Mathematical Surveys and Monographs 96, Amer. Math. Soc. 2002. x+349 pp. MR2003f:18011(for Feynman transform see page 251)