Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems

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.

Appendix A overlaps with arXiv:1506.04652. In this appendix, some basic facts about jet bundles and variational bicomplex are collected

References in corpus (2)

• Supergroupoids, double structures, and equivariant cohomology
• Presymplectic structures and intrinsic Lagrangians

Cited by in corpus (6)

• Covariant canonical formulations of classical field theories
• Higher Spin Gravities and Presymplectic AKSZ Models
• BV equivalence with boundary
• Presymplectic gauge PDEs and Lagrangian BV formalism beyond jet-bundles
• Lie and Leibniz Algebras of Lower-Degree Conservation Laws
• Consistent deformations in the presymplectic BV-AKSZ approach