engleski

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 θ µν, 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(µ 2 (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 θ µν 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 divergencefree result for the one-loop quantum corrections, having also both well-defined commutative limit and point-like limit of an extended object.

non-commutative geometry; photon and neutrino physics; non-perturbative effects

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