Symmetries and Noether's theorem for multicontact field theories

Fuente: arXiv
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Autores principales: Rivas, Xavier, Román-Roy, Narciso, Zawora, Bartosz M.
Formato: Preprint
Publicado: 2025
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_version_ 1866929742831157248
author Rivas, Xavier
Román-Roy, Narciso
Zawora, Bartosz M.
author_facet Rivas, Xavier
Román-Roy, Narciso
Zawora, Bartosz M.
contents A geometric framework, called multicontact geometry, has recently been developed to study action-dependent field theories. In this work, we use this framework to analyze symmetries in action-dependent Lagrangian and Hamiltonian field theories, as well as their associated dissipation laws. Specifically, we establish the definitions of conserved and dissipated quantities, define the general symmetries of the field equations and the geometric structure, and examine their properties. The latter ones, referred to as Noether symmetries, lead to the formulation of a version of Noether's Theorem in this setting, which associates each of these symmetries with the corresponding dissipated quantity and the resulting conservation law.
format Preprint
id arxiv_https___arxiv_org_abs_2503_03463
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Symmetries and Noether's theorem for multicontact field theories
Rivas, Xavier
Román-Roy, Narciso
Zawora, Bartosz M.
Mathematical Physics
53D42, 70S20, 35B06, 53D10, 53Z05, 70S10
A geometric framework, called multicontact geometry, has recently been developed to study action-dependent field theories. In this work, we use this framework to analyze symmetries in action-dependent Lagrangian and Hamiltonian field theories, as well as their associated dissipation laws. Specifically, we establish the definitions of conserved and dissipated quantities, define the general symmetries of the field equations and the geometric structure, and examine their properties. The latter ones, referred to as Noether symmetries, lead to the formulation of a version of Noether's Theorem in this setting, which associates each of these symmetries with the corresponding dissipated quantity and the resulting conservation law.
title Symmetries and Noether's theorem for multicontact field theories
topic Mathematical Physics
53D42, 70S20, 35B06, 53D10, 53Z05, 70S10
url https://arxiv.org/abs/2503.03463