Two-Point Functions on Deformed Spacetime
We present a review of the one-loop photon (Π) and neutrino (Σ) two-point functions in a covariant and deformed U(1) gauge-theory on the 4-dimensional noncommutative spaces, determined by a constant antisymmetric tensor θμν, and by a parameter-space (κf,κg), respectively. For the general fermion-pho...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2014 |
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Інститут математики НАН України
2014
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146685 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Two-Point Functions on Deformed Spacetime / J. Trampetić, J. You // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 75 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862537107394789376 |
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| author | Trampetić, J. You, J. |
| author_facet | Trampetić, J. You, J. |
| citation_txt | Two-Point Functions on Deformed Spacetime / J. Trampetić, J. You // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 75 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present a review of the one-loop photon (Π) and neutrino (Σ) two-point functions in a covariant and deformed U(1) gauge-theory on the 4-dimensional noncommutative spaces, determined by a constant antisymmetric tensor θμν, and by a parameter-space (κf,κg), respectively. For the general fermion-photon Sf(κf) and photon self-interaction Sg(κg) the closed form results reveal two-point functions with all kind of pathological terms: the UV divergence, the quadratic UV/IR mixing terms as well as a logarithmic IR divergent term of the type ln(μ²(θp)²). In addition, the photon-loop produces new tensor structures satisfying transversality condition by themselves. We show that the photon two-point function in the 4-dimensional Euclidean spacetime can be reduced to two finite terms by imposing a specific full rank of θμν and setting deformation parameters (κf,κg)=(0,3). In this case the neutrino two-point function vanishes. Thus for a specific point (0,3) in the parameter-space (κf,κg), a covariant θ-exact approach is able to produce a divergence-free result for the one-loop quantum corrections, having also both well-defined commutative limit and point-like limit of an extended object.
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| first_indexed | 2025-11-24T11:38:35Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146685 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T11:38:35Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
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| spelling | Trampetić, J. You, J. 2019-02-10T18:13:01Z 2019-02-10T18:13:01Z 2014 Two-Point Functions on Deformed Spacetime / J. Trampetić, J. You // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 75 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R60; 81T10; 81T15 DOI:10.3842/SIGMA.2014.054 https://nasplib.isofts.kiev.ua/handle/123456789/146685 We present a review of the one-loop photon (Π) and neutrino (Σ) two-point functions in a covariant and deformed U(1) gauge-theory on the 4-dimensional noncommutative spaces, determined by a constant antisymmetric tensor θμν, and by a parameter-space (κf,κg), respectively. For the general fermion-photon Sf(κf) and photon self-interaction Sg(κg) the closed form results reveal two-point functions with all kind of pathological terms: the UV divergence, the quadratic UV/IR mixing terms as well as a logarithmic IR divergent term of the type ln(μ²(θp)²). In addition, the photon-loop produces new tensor structures satisfying transversality condition by themselves. We show that the photon two-point function in the 4-dimensional Euclidean spacetime can be reduced to two finite terms by imposing a specific full rank of θμν and setting deformation parameters (κf,κg)=(0,3). In this case the neutrino two-point function vanishes. Thus for a specific point (0,3) in the parameter-space (κf,κg), a covariant θ-exact approach is able to produce a divergence-free result for the one-loop quantum corrections, having also both well-defined commutative limit and point-like limit of an extended object. This paper is a contribution to the Special Issue on Deformations of Space-Time and its Symmetries. The
 full collection is available at http://www.emis.de/journals/SIGMA/space-time.html. 
 J.T. would like to acknowledge J. Erdmenger and W. Hollik for discussions, and Max-PlanckInstitute
 for Physics, Munich, for hospitality. A great deal of computation was done by using
 Mathematica 8.0⁴ and tensor algebra package xAct⁵
 . en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Two-Point Functions on Deformed Spacetime Article published earlier |
| spellingShingle | Two-Point Functions on Deformed Spacetime Trampetić, J. You, J. |
| title | Two-Point Functions on Deformed Spacetime |
| title_full | Two-Point Functions on Deformed Spacetime |
| title_fullStr | Two-Point Functions on Deformed Spacetime |
| title_full_unstemmed | Two-Point Functions on Deformed Spacetime |
| title_short | Two-Point Functions on Deformed Spacetime |
| title_sort | two-point functions on deformed spacetime |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146685 |
| work_keys_str_mv | AT trampeticj twopointfunctionsondeformedspacetime AT youj twopointfunctionsondeformedspacetime |