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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2016 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147863 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862687279375450112 |
|---|---|
| author | Sharapov, A.A. |
| author_facet | Sharapov, A.A. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T16:06:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147863 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:06:04Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sharapov, A.A. 2019-02-16T09:32:31Z 2019-02-16T09:32:31Z 2016 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 https://nasplib.isofts.kiev.ua/handle/123456789/147863 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. The work was partially supported by the RFBR grant No. 16-02-00284 A. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems Article published earlier |
| spellingShingle | Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems Sharapov, A.A. |
| title | 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_short | Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems |
| title_sort | variational tricomplex, global symmetries and conservation laws of gauge systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147863 |
| work_keys_str_mv | AT sharapovaa variationaltricomplexglobalsymmetriesandconservationlawsofgaugesystems |