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<p>A geometric framework, called <i>multicontact geometry</i>, 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 <i>Noether symmetries</i>, 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.</p>

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Symmetries and Noether’s theorem for action-dependent multicontact field theories

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月30日

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  • Xavier Rivas,
  • Narciso Román-Roy,
  • Bartosz M. Zawora

摘要

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.