More insights into symmetries in multisymplectic field theories

TL;DR

This paper offers a comprehensive overview of symmetries in classical field theories within (pre)multisymplectic geometry, clarifying their geometric interpretation and analyzing their structure in constrained, singular theories.

Contribution

It provides a unified geometric framework for understanding symmetries in classical field theories and explores their structure in the context of constraints and singularities.

Findings

Clarified the geometric interpretation of symmetries in field theories

Analyzed symmetries in constrained and singular theories

Constructed multimomentum maps for typical physical theories

Abstract

This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics and in the geometric formulation of these theories are clarified. Finally, a general discussion is given on the structure of symmetries in the presence of constraints appearing in singular field theories. Symmetries of some typical theories in theoretical physics are analyzed through the construction of the relevant multimomentum maps which are the conserved quantities (by Noether's theorem) on the (pre)multisymplectic phase spaces.