Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems

TL;DR

This paper develops a generalized framework using variational tricomplexes to connect symmetries and conservation laws in gauge systems, extending Noether's theorem to lower-degree laws.

Contribution

It introduces a new approach to relate gauge symmetries with a hierarchy of conservation laws via the variational tricomplex and establishes a Lie algebra structure among conservation laws.

Findings

Generalized symmetries lead to sequences of conservation laws.

Extension of Noether's correspondence to lower-degree laws.

Lie algebra structure on conservation laws and symmetries.

Abstract

Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are represented by on-shell closed forms of various degrees. This extends the usual Noether's correspondence between global symmetries and conservation laws to the case of lower-degree conservation laws and not necessarily variational equations of motion. Finally, we equip the space of conservation laws of a given degree with a Lie bracket and establish a homomorphism of the resulting Lie algebra to the Lie algebra of global symmetries.