Symmetry Factors of Feynman Diagrams and the Homological Perturbation Lemma

Christian Saemann; Emmanouil Sfinarolakis

Symmetry Factors of Feynman Diagrams and the Homological Perturbation Lemma

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arxiv 2009.12616 v1 pith:HIZOBQMC submitted 2020-09-26 hep-th math-phmath.MP

Christian Saemann , Emmanouil Sfinarolakis This is my paper · ORCID

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keywords feynmansymmetrydiagramsfactorshomologicallemmaperturbationamplitudes

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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.

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Full S-matrices and Witten diagrams with (relative) L-infinity algebras
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Cyclic relative L-infinity algebras encode the full S-matrix, including its trivial part, and reproduce Witten diagrams including CFT two-point functions.

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