Space-Time Diffeomorphisms in Noncommutative Gauge Theories
In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very conv...
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| Cite this: | Space-Time Diffeomorphisms in Noncommutative Gauge Theories / M. Rosenbaum, J.D. Vergara, L.R. Juarez // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 34 назв. — англ. |
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Rosenbaum, M. Vergara, J.D. Juarez, L.R. 2019-02-19T13:08:28Z 2019-02-19T13:08:28Z 2008 Space-Time Diffeomorphisms in Noncommutative Gauge Theories / M. Rosenbaum, J.D. Vergara, L.R. Juarez // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 34 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 70S10; 70S05; 81T75 https://nasplib.isofts.kiev.ua/handle/123456789/149026 In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics) where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985), 288–315, 316–333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987), 319–328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times. This paper is a contribution to the Special Issue on Deformation Quantization. The authors are grateful to Prof. Karel Kuchaˇr for fruitful discussions and clarifications concerning his work on parametrized canonical quantization. They are also grateful to the referees for some very pertinent comments and suggestions which helped to clarify considerably some points in the manuscript. The authors also acknowledge partial support from CONACyT projects UA7899-F (M.R.) and 47211-F (J.D.V.) and DGAPA-UNAM grant IN109107 (J.D.V.). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Space-Time Diffeomorphisms in Noncommutative Gauge Theories Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Space-Time Diffeomorphisms in Noncommutative Gauge Theories |
| spellingShingle |
Space-Time Diffeomorphisms in Noncommutative Gauge Theories Rosenbaum, M. Vergara, J.D. Juarez, L.R. |
| title_short |
Space-Time Diffeomorphisms in Noncommutative Gauge Theories |
| title_full |
Space-Time Diffeomorphisms in Noncommutative Gauge Theories |
| title_fullStr |
Space-Time Diffeomorphisms in Noncommutative Gauge Theories |
| title_full_unstemmed |
Space-Time Diffeomorphisms in Noncommutative Gauge Theories |
| title_sort |
space-time diffeomorphisms in noncommutative gauge theories |
| author |
Rosenbaum, M. Vergara, J.D. Juarez, L.R. |
| author_facet |
Rosenbaum, M. Vergara, J.D. Juarez, L.R. |
| publishDate |
2008 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics) where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985), 288–315, 316–333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987), 319–328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149026 |
| citation_txt |
Space-Time Diffeomorphisms in Noncommutative Gauge Theories / M. Rosenbaum, J.D. Vergara, L.R. Juarez // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 34 назв. — англ. |
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2025-12-01T14:52:25Z |
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2025-12-01T14:52:25Z |
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1850860552520204288 |