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arXiv · 1903.05643

The $L_\infty$-algebra of the S-matrix

Alex S. Arvanitakis
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Abstract

We point out that the one-particle-irreducible vacuum correlation functions of a QFT are the structure constants of an $L_\infty$-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 $L_\infty$-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 recent work).

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Alex S. Arvanitakis. 2019-03-13. The $L_\infty$-algebra of the S-matrix. https://arxiv.org/abs/1903.05643

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