Towards Unifying Structures in Higher Spin Gauge Symmetry
This article is expository in nature, outlining some of the many still incompletely understood features of higher spin field theory. We are mainly considering higher spin gauge fields in their own right as free-standing theoretical constructs and not circumstances where they occur as part of another...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2008 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2008
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148986 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Towards Unifying Structures in Higher Spin Gauge Symmetry / Anders K.H. Bengtsson // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 79 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862572537085427712 |
|---|---|
| author | Bengtsson, Anders K.H. |
| author_facet | Bengtsson, Anders K.H. |
| citation_txt | Towards Unifying Structures in Higher Spin Gauge Symmetry / Anders K.H. Bengtsson // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 79 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This article is expository in nature, outlining some of the many still incompletely understood features of higher spin field theory. We are mainly considering higher spin gauge fields in their own right as free-standing theoretical constructs and not circumstances where they occur as part of another system. Considering the problem of introducing interactions among higher spin gauge fields, there has historically been two broad avenues of approach. One approach entails gauging a non-Abelian global symmetry algebra, in the process making it local. The other approach entails deforming an already local but Abelian gauge algebra, in the process making it non-Abelian. In cases where both avenues have been explored, such as for spin 1 and 2 gauge fields, the results agree (barring conceptual and technical issues) with Yang-Mills theory and Einstein gravity. In the case of an infinite tower of higher spin gauge fields, the first approach has been thoroughly developed and explored by M. Vasiliev, whereas the second approach, after having lain dormant for a long time, has received new attention by several authors lately. In the present paper we briefly review some aspects of the history of higher spin gauge fields as a backdrop to an attempt at comparing the gauging vs. deforming approaches. A common unifying structure of strongly homotopy Lie algebras underlying both approaches will be discussed. The modern deformation approach, using BRST-BV methods, will be described as far as it is developed at the present time. The first steps of a formulation in the categorical language of operads will be outlined. A few aspects of the subject that seems not to have been thoroughly investigated are pointed out.
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| first_indexed | 2025-11-26T05:09:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148986 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T05:09:17Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bengtsson, Anders K.H. 2019-02-19T12:44:21Z 2019-02-19T12:44:21Z 2008 Towards Unifying Structures in Higher Spin Gauge Symmetry / Anders K.H. Bengtsson // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 79 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 70S10; 70S20; 70G60; 70H45; 81T13; 81T70 https://nasplib.isofts.kiev.ua/handle/123456789/148986 This article is expository in nature, outlining some of the many still incompletely understood features of higher spin field theory. We are mainly considering higher spin gauge fields in their own right as free-standing theoretical constructs and not circumstances where they occur as part of another system. Considering the problem of introducing interactions among higher spin gauge fields, there has historically been two broad avenues of approach. One approach entails gauging a non-Abelian global symmetry algebra, in the process making it local. The other approach entails deforming an already local but Abelian gauge algebra, in the process making it non-Abelian. In cases where both avenues have been explored, such as for spin 1 and 2 gauge fields, the results agree (barring conceptual and technical issues) with Yang-Mills theory and Einstein gravity. In the case of an infinite tower of higher spin gauge fields, the first approach has been thoroughly developed and explored by M. Vasiliev, whereas the second approach, after having lain dormant for a long time, has received new attention by several authors lately. In the present paper we briefly review some aspects of the history of higher spin gauge fields as a backdrop to an attempt at comparing the gauging vs. deforming approaches. A common unifying structure of strongly homotopy Lie algebras underlying both approaches will be discussed. The modern deformation approach, using BRST-BV methods, will be described as far as it is developed at the present time. The first steps of a formulation in the categorical language of operads will be outlined. A few aspects of the subject that seems not to have been thoroughly investigated are pointed out. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). Work partly supported by the Research and Education Board at the University College of Bor˚as. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Towards Unifying Structures in Higher Spin Gauge Symmetry Article published earlier |
| spellingShingle | Towards Unifying Structures in Higher Spin Gauge Symmetry Bengtsson, Anders K.H. |
| title | Towards Unifying Structures in Higher Spin Gauge Symmetry |
| title_full | Towards Unifying Structures in Higher Spin Gauge Symmetry |
| title_fullStr | Towards Unifying Structures in Higher Spin Gauge Symmetry |
| title_full_unstemmed | Towards Unifying Structures in Higher Spin Gauge Symmetry |
| title_short | Towards Unifying Structures in Higher Spin Gauge Symmetry |
| title_sort | towards unifying structures in higher spin gauge symmetry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148986 |
| work_keys_str_mv | AT bengtssonanderskh towardsunifyingstructuresinhigherspingaugesymmetry |