Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology
In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincaré invariance. We present the latest development in the field, in particular the notion of equivalence of such quantum field theories on a noncommutative spacetime...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2010 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146355 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology / A.P. Balachandran, A. Ibort, G. Marmo, M. Martone // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 70 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859688920441159680 |
|---|---|
| author | Balachandran, A.P. Ibort, A. Marmo, G. Martone, M. |
| author_facet | Balachandran, A.P. Ibort, A. Marmo, G. Martone, M. |
| citation_txt | Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology / A.P. Balachandran, A. Ibort, G. Marmo, M. Martone // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 70 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincaré invariance. We present the latest development in the field, in particular the notion of equivalence of such quantum field theories on a noncommutative spacetime, in this regard we work out explicitly the inequivalence between twisted quantum field theories on Moyal and Wick-Voros planes; the duality between deformations of the multiplication map on the algebra of functions on spacetime F(R⁴) and coproduct deformations of the Poincaré-Hopf algebra HP acting on F(R⁴); the appearance of a nonassociative product on F(R⁴) when gauge fields are also included in the picture. The last part of the manuscript is dedicated to the phenomenology of noncommutative quantum field theories in the particular approach adopted in this review. CPT violating processes, modification of two-point temperature correlation function in CMB spectrum analysis and Pauli-forbidden transition in Be4 are all effects which show up in such a noncommutative setting. We review how they appear and in particular the constraint we can infer from comparison between theoretical computations and experimental bounds on such effects. The best bound we can get, coming from Borexino experiment, is >10²⁴ TeV for the energy scale of noncommutativity, which corresponds to a length scale <10⁻⁴³ m. This bound comes from a different model of spacetime deformation more adapted to applications in atomic physics. It is thus model dependent even though similar bounds are expected for the Moyal spacetime as well as argued elsewhere.
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| first_indexed | 2025-11-30T23:10:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146355 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T23:10:35Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Balachandran, A.P. Ibort, A. Marmo, G. Martone, M. 2019-02-09T09:30:58Z 2019-02-09T09:30:58Z 2010 Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology / A.P. Balachandran, A. Ibort, G. Marmo, M. Martone // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 70 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R50; 81R60 DOI:10.3842/SIGMA.2010.052 https://nasplib.isofts.kiev.ua/handle/123456789/146355 In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincaré invariance. We present the latest development in the field, in particular the notion of equivalence of such quantum field theories on a noncommutative spacetime, in this regard we work out explicitly the inequivalence between twisted quantum field theories on Moyal and Wick-Voros planes; the duality between deformations of the multiplication map on the algebra of functions on spacetime F(R⁴) and coproduct deformations of the Poincaré-Hopf algebra HP acting on F(R⁴); the appearance of a nonassociative product on F(R⁴) when gauge fields are also included in the picture. The last part of the manuscript is dedicated to the phenomenology of noncommutative quantum field theories in the particular approach adopted in this review. CPT violating processes, modification of two-point temperature correlation function in CMB spectrum analysis and Pauli-forbidden transition in Be4 are all effects which show up in such a noncommutative setting. We review how they appear and in particular the constraint we can infer from comparison between theoretical computations and experimental bounds on such effects. The best bound we can get, coming from Borexino experiment, is >10²⁴ TeV for the energy scale of noncommutativity, which corresponds to a length scale <10⁻⁴³ m. This bound comes from a different model of spacetime deformation more adapted to applications in atomic physics. It is thus model dependent even though similar bounds are expected for the Moyal spacetime as well as argued elsewhere. This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The full collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html. It is a pleasure for Balachandran, Marmo and Martone to thank Alberto Ibort and the Universidad Carlos III de Madrid for their wonderful hospitality and support. The work of Balachandran and Martone was supported in part by DOE under the grant number DE-FG02-85ER40231 and by the Institute of Mathematical Sciences, Chennai. We thank Professor T.R. Govindarajan for his wonderful hospitality at Chennai. Balachandran was also supported by the Department of Science and Technology, India. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology Article published earlier |
| spellingShingle | Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology Balachandran, A.P. Ibort, A. Marmo, G. Martone, M. |
| title | Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology |
| title_full | Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology |
| title_fullStr | Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology |
| title_full_unstemmed | Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology |
| title_short | Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology |
| title_sort | quantum fields on noncommutative spacetimes: theory and phenomenology |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146355 |
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