The L ∞-algebra of the S-matrix

Alex Arvanitakis (The Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 2AZ, U.K.)

We point out that the one-particle-irreducible vacuum correlation functions of a QFT are the structure constants of an L ∞-algebra, whose Jacobi identities hold whenever there are no local gauge anomalies. The LSZ prescription for S-matrix elements is identified as an instance of the “minimal model theorem” of L ∞-algebras. This generalises the algebraic structure of closed string field theory to arbitrary QFTs with a mass gap and leads to recursion relations for amplitudes (albeit ones only immediately useful at tree-level, where they reduce to Berends-Giele-style relations as shown in [1]).

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      "value": "We point out that the one-particle-irreducible vacuum correlation functions of a QFT are the structure constants of an L \u221e-algebra, whose Jacobi identities hold whenever there are no local gauge anomalies. The LSZ prescription for S-matrix elements is identified as an instance of the \u201cminimal model theorem\u201d of L \u221e-algebras. This generalises the algebraic structure of closed string field theory to arbitrary QFTs with a mass gap and leads to recursion relations for amplitudes (albeit ones only immediately useful at tree-level, where they reduce to Berends-Giele-style relations as shown in [1])."
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Published on:
13 December 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2019 (2019)
Issue 7
Pages 1-25
DOI:
https://doi.org/10.1007/JHEP07(2019)115
arXiv:
1903.05643
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: