On the notion of gauge symmetries of generic Lagrangian field theory
| Autor: | Giachetta, G., Mangiarotti, L., Sardanashvily, G. |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | J.Math.Phys.50:012903,2009 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.3049750 |
| Popis: | 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. Comment: 27 pages, accepted for publication in J. Math. Phys |
| Databáze: | arXiv |
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