engleski

Self-energies on deformed spacetimes

We study one-loop photon (Π) and neutrino (Σ) self-energies in a U(1) covariant gauge-theory on d-dimensional noncommutative spaces determined by a antisymmetric-constant tensor θ^{; ; μν}; ; . For the general fermion-photon (S_f ) and photon self-interaction (S_g ) the closed form results reveal self-energies besetting 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 self-energy in four-dimensional Euclidean space-time can be reduced to two finite terms by imposing a specific full rank of θ μν and setting parameters (κ_f , κ_g ) = (0, 3). In this case the neutrino two-point function vanishes. Thus for a specific point (0, 3) in the parameter-space (κ_f , κ_g ), a covariant θ-exact approach is able to produce a divergence-free result for one-loop quantum corrections, having also well-defined both the commutative limit as well as the pointlike limit of an extended object. While in two-dimensional space the photon self-energy is finite for arbitrary (κ_f , κ_g ) combinations, the neutrino self-energy still contains an superficial IR divergence.

non-commutative geometry; photon and neutrino physics; nonpertubative physics

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