Perturbative Quantum Field Theory and Homotopy Algebras

Saemann, Christian, Jurco, Branislav, Kim, Hyungrok, Macrelli, Tommaso and Wolf, Martin (2020) Perturbative Quantum Field Theory and Homotopy Algebras In: Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019) - Workshop on Quantum Geometry, Field Theory and Gravity, 25-29 Sep 2019, Corfu, Greece.

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Abstract

We review the homotopy algebraic perspective on perturbative quantum field theory: classical field theories correspond to homotopy algebras such as A∞- and L∞-algebras. Furthermore, their scattering amplitudes are encoded in minimal models of these homotopy algebras at tree level and their quantum relatives at loop level. The translation between Lagrangian field theories and homotopy algebras is provided by the Batalin-Vilkovisky formalism. The minimal models are computed recursively using the homological perturbation lemma, which induces useful recursion relations for the computation of scattering amplitudes. After explaining how the homolcogical perturbation lemma produces the usual Feynman diagram expansion, we use our techniques to verify an identity for the Berends-Giele currents which implies the Kleiss-Kuijf relations.

Item Type:	Conference or Workshop Item (Conference Paper)
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Name Email ORCID Saemann, Christian Jurco, Branislav Kim, Hyungrok Macrelli, Tommaso t.macrelli@surrey.ac.uk Wolf, Martin m.wolf@surrey.ac.uk
Date :	18 August 2020
DOI :	10.22323/1.376.0199
Copyright Disclaimer :	Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Depositing User :	Clive Harris
Date Deposited :	03 Sep 2020 15:56
Last Modified :	03 Sep 2020 15:56
URI:	http://epubs.surrey.ac.uk/id/eprint/858532

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