Perturbative Quantum Field Theory and Homotopy Algebras

Branislav Jurco, Hyungrok Kim, Tommaso Macrelli, Christian Saemann, Martin Wolf

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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.
Original languageEnglish
Article number199
JournalProceedings of Science
Publication statusPublished - 18 Aug 2020
EventCorfu Summer Institute 2019: School and Workshops on Elementary Particle Physics and Gravity - Corfu, Greece
Duration: 25 Sept 201929 Sept 2019


  • hep-th
  • math-ph
  • math.MP


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