Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere
We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present som...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2006 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2006
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146086 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere / M. Panero // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 88 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862710250090528768 |
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| author | Panero, M. |
| author_facet | Panero, M. |
| citation_txt | Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere / M. Panero // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 88 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution.
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| first_indexed | 2025-12-07T17:23:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146086 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:23:13Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Panero, M. 2019-02-07T09:12:30Z 2019-02-07T09:12:30Z 2006 Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere / M. Panero // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 88 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 58B34; 81R60 https://nasplib.isofts.kiev.ua/handle/123456789/146086 We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution. This paper is a contribution to the Proceedings of the O’Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 22–24, 2006, Budapest, Hungary). The author thanks the organisers of the O’Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 22–24, 2006, Budapest, Hungary) for the stimulating and really enjoyable atmosphere at the conference, as well as A.P. Balachandran, W. Bietenholz, B.P. Dolan, K.S. Gupta, D. O’Connor and H. Steinacker for enlightening discussions. This work is supported by Enterprise Ireland under the Basic Research Programme. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere Article published earlier |
| spellingShingle | Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere Panero, M. |
| title | Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere |
| title_full | Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere |
| title_fullStr | Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere |
| title_full_unstemmed | Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere |
| title_short | Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere |
| title_sort | quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146086 |
| work_keys_str_mv | AT panerom quantumfieldtheoryinanoncommutativespacetheoreticalpredictionsandnumericalresultsonthefuzzysphere |