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arXiv · 0807.3003

On the notion of gauge symmetries of generic Lagrangian field theory

G. Giachetta·L. Mangiarotti·G. Sardanashvily
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Abstract

General Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Its non-trivial reducible gauge symmetries and their algebra are defined in this very general setting by means of the inverse second Noether theorem. In contrast with gauge symmetries, non-trivial Noether and higher-stage Noether identities of Lagrangian theory can be intrinsically defined by constructing the exact Koszul-Tate complex. The inverse second Noether theorem that we prove associates to this complex the cochain sequence with the ascent operator whose components define non-trivial gauge and higher-stage gauge symmetries. These gauge symmetries are said to be algebraically closed if the ascent operator can be extended to a nilpotent operator. The necessary conditions for this extension are stated. The characteristic examples of Yang-Mills supergauge theory, topological Chern-Simons theory, gauge gravitation theory and topological BF theory are presented.

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G. Giachetta, L. Mangiarotti, G. Sardanashvily. 2008-11-25. On the notion of gauge symmetries of generic Lagrangian field theory. https://doi.org/10.1063/1.3049750

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