The homotopy momentum map of general relativity

2021/03/13 by Christian Blohmann, Blohmann, Christian · 2 citations
Mathematics · Physics and Astronomy · #18N40 #37K06 #53D20 #83C05 #Advanced Topics in Algebra #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2103.07670

openalex publication_date 2021/03/13 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We show that the action of spacetime vector fields on the variational bicomplex of general relativity has a homotopy momentum map that extends the map from vector fields to conserved currents given by Noether's first theorem to a morphism of L_∞-algebras.

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• Multisymplectic observable reduction using constraint triples
• Homotopy reduction of multisymplectic structures in Lagrangian field theory

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