Two-Point Functions on Deformed Spacetime

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2014
• Hauptverfasser: Trampetić, J., You, J.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут математики НАН України 2014
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/146685
• 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.

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.