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October 9, 2025Open Access

Homotopy reduction of multisymplectic structures in Lagrangian field theory

Key Points

The study develops methods for homotopy reduction of multisymplectic structures in Lagrangian field theory, enhancing the geometric understanding of physical systems.
Key evidence includes the introduction of homotopy momentum maps as morphisms of $L_ ext{infinity}$-algebras, which reshapes the framework of field theories.
The methodological approach focuses on local homotopy momentum maps and utilizes algebraic structures in the context of multisymplectic geometry.
This work highlights new avenues for exploration in the geometric aspects of classical mechanics, necessitating further research in this area.

Abstract

While symplectic geometry is the geometric framework of classical mechanics, the geometry of classical field theories is governed by multisymplectic structures. In multisymplectic geometry, the Poisson algebra of Hamiltonian functions is replaced by the L_-algebra of Hamiltonian forms introduced by Rogers in 2012. The corresponding notion of homotopy momentum maps as morphisms of L_-algebras is due to Callies, Fr\'egier, Rogers, and Zambon in 2016. We develop a method of homotopy reduction for local homotopy momentum maps in Lagrangian field theory using these homotopy algebraic structures.

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Cite This Study

Janina Bernardy (Wed,) studied this question.

synapsesocial.com/papers/68e8439a9989581a2fd4e02f https://doi.org/https://doi.org/10.48550/arxiv.2505.09492

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