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Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems

Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems

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. Th...

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Main Author: Sharapov, A.A.
Format: Article
Language:English
Published: Інститут математики НАН України 2016
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147863
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spelling irk-123456789-1478632019-02-17T01:23:19Z Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems Sharapov, A.A. 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. 2016 Article Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems / A.A. Sharapov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 35 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70S10; 81T70; 83C40 DOI:10.3842/SIGMA.2016.098 http://dspace.nbuv.gov.ua/handle/123456789/147863 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description 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.
format Article
author Sharapov, A.A.
spellingShingle Sharapov, A.A.
Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Sharapov, A.A.
author_sort Sharapov, A.A.
title Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems
title_short Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems
title_full Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems
title_fullStr Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems
title_full_unstemmed Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems
title_sort variational tricomplex, global symmetries and conservation laws of gauge systems
publisher Інститут математики НАН України
publishDate 2016
url http://dspace.nbuv.gov.ua/handle/123456789/147863
citation_txt Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems / A.A. Sharapov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 35 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT sharapovaa variationaltricomplexglobalsymmetriesandconservationlawsofgaugesystems
first_indexed 2023-05-20T17:28:42Z
last_indexed 2023-05-20T17:28:42Z
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