Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 098, 24 pages      arXiv:1607.01626

Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems

Alexey A. Sharapov
Physics Faculty, Tomsk State University, Lenin ave. 36, Tomsk 634050, Russia

Received July 12, 2016, in final form September 30, 2016; Published online October 03, 2016

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.

Key words: variational bicomplex; BRST differential; presymplectic structure; lower-degree conservation laws.

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