Symmetry Factors of Feynman Diagrams and the Homological Perturbation Lemma

Abstract

We discuss the symmetry factors of Feynman diagrams of scalar field theories with polynomial potential. After giving a concise general formula for them, we present an elementary and direct proof that when computing scattering amplitudes using the homological perturbation lemma, each contributing Feynman diagram is indeed included with the correct symmetry factor.

arXiv comment20 pages

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• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• Extremal Black Holes from Homotopy Algebras
• Ambitwistor Yang-Mills Theory Revisited