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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| Datum: | 2016 |
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| Sprache: | English |
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Інститут математики НАН України
2016
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147863 |
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| Zitieren: | 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. |
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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 |
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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 |
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| first_indexed |
2025-07-11T02:59:08Z |
| last_indexed |
2025-07-11T02:59:08Z |
| _version_ |
1837317751383785472 |