Multisymplectic observable reduction using constraint triples

2025/05/30 by Miti, Antonio Michele, Ryvkin, Leonid
#16W50 (secondary) #53D20 (primary) 53D05 #Differential Geometry (math.DG) #FOS: Mathematics #Rings and Algebras (math.RA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2506.00234

Abstract

The purpose of this paper is to present a fully algebraic formalism for the construction and reduction of L_∞-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).

Citations

• Homotopy reduction of multisymplectic structures in Lagrangian field theory
• Marsden--Meyer--Weinstein reduction for k-contact field theories
• The homotopy momentum map of general relativity
• Multisymplectic Structures and Higher Momentum Maps
• An invitation to multisymplectic geometry
• Gerstenhaber and Batalin-Vilkovisky structures on modules over operads
• Lie Infinity-Algebras from Lie Rinehart Pairs
• Homotopy moment maps
• Batalin-Vilkovisky Structures on Ext and Tor

Related

• The notion of Observables in Multisymplectic Geometry
• Multisymplectic Structures and Higher Momentum Maps
• On Types of Observables in Constrained Theories
• On a Multisymplectic Formulation of the Classical BRST symmetry for First Order Field Theories Part I: Algebraic Structures
• The quantization of constrained systems: from symplectic reduction to Rieffel induction