Multisymplectic observable reduction using constraint triples

TL;DR

This paper develops an algebraic framework for reducing multisymplectic observables using $L_$-algebras, Gerstenhaber algebras, and constraint triples, clarifying recent geometric results.

Contribution

It introduces a fully algebraic formalism for multisymplectic observable reduction, extending previous geometric approaches with new algebraic tools.

Findings

Reconstruction of recent geometric results in algebraic terms

Formalism unifies various algebraic structures in multisymplectic geometry

Provides a conceptual explanation for observable reduction methods

Abstract

The purpose of this paper is to present a fully algebraic formalism for the construction and reduction of $L_\infty$-algebras of observables inspired by multisymplectic geometry, using Gerstenhaber algebras, BV-modules, and the constraint triple formalism. In the "geometric case", we reconstruct and conceptually explain the recent results of arXiv:2206.03137(3).