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
Datum:2014
Hauptverfasser: Trampetić, J., You, J.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2014
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146685
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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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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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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