Field Theory with Coordinate Dependent Noncommutativity
We discuss the formulation of classical field theoretical models on n-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field theories in noncommutative space-time to obtain local conserv...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209871 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Field Theory with Coordinate Dependent Noncommutativity / D.N. Blaschke, F. Gieres, S. Hohenegger, M. Schweda, M. Wohlgenannt // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 111 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862733888481132544 |
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| author | Blaschke, D.N. Gieres, F. Hohenegger, S. Schweda, M. Wohlgenannt, M. |
| author_facet | Blaschke, D.N. Gieres, F. Hohenegger, S. Schweda, M. Wohlgenannt, M. |
| citation_txt | Field Theory with Coordinate Dependent Noncommutativity / D.N. Blaschke, F. Gieres, S. Hohenegger, M. Schweda, M. Wohlgenannt // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 111 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We discuss the formulation of classical field theoretical models on n-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field theories in noncommutative space-time to obtain local conservation laws (for the electric charge and for the energy-momentum tensor of free fields) and, more generally, an energy-momentum balance equation for interacting fields. For free field models, an analogy with the damped harmonic oscillator in classical mechanics is pointed out, which allows us to get a physical understanding of the obtained conservation laws. To conclude, the formulation of field theories on curved noncommutative space is addressed.
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| first_indexed | 2025-12-07T19:39:49Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209871 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:39:49Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Blaschke, D.N. Gieres, F. Hohenegger, S. Schweda, M. Wohlgenannt, M. 2025-11-28T09:37:06Z 2018 Field Theory with Coordinate Dependent Noncommutativity / D.N. Blaschke, F. Gieres, S. Hohenegger, M. Schweda, M. Wohlgenannt // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 111 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81T75; 70H33; 81T13; 51P05; 81T75 arXiv: 1806.02131 https://nasplib.isofts.kiev.ua/handle/123456789/209871 https://doi.org/10.3842/SIGMA.2018.133 We discuss the formulation of classical field theoretical models on n-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field theories in noncommutative space-time to obtain local conservation laws (for the electric charge and for the energy-momentum tensor of free fields) and, more generally, an energy-momentum balance equation for interacting fields. For free field models, an analogy with the damped harmonic oscillator in classical mechanics is pointed out, which allows us to get a physical understanding of the obtained conservation laws. To conclude, the formulation of field theories on curved noncommutative space is addressed. The authors are indebted to H. Grosse, C. Roger, V. Kupriyanov, M. Dobrski, and H. Steinacker for reading a preliminary version of our manuscript and for their instructive remarks on some of the mathematical aspects. We are also grateful to the anonymous referees for their important remarks. We sincerely thank D. Grumiller, K. Landsteiner, and A. Rebhan for organizing a memorial meeting in the memory of Manfred Schweda at the Vienna University of Technology and for inviting us to present our joint work with Manfred on that occasion. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Field Theory with Coordinate Dependent Noncommutativity Article published earlier |
| spellingShingle | Field Theory with Coordinate Dependent Noncommutativity Blaschke, D.N. Gieres, F. Hohenegger, S. Schweda, M. Wohlgenannt, M. |
| title | Field Theory with Coordinate Dependent Noncommutativity |
| title_full | Field Theory with Coordinate Dependent Noncommutativity |
| title_fullStr | Field Theory with Coordinate Dependent Noncommutativity |
| title_full_unstemmed | Field Theory with Coordinate Dependent Noncommutativity |
| title_short | Field Theory with Coordinate Dependent Noncommutativity |
| title_sort | field theory with coordinate dependent noncommutativity |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209871 |
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