First-order processes of the de Sitter QED in the rest frame vacuum - Ion I. Cotăescu (European Physical Journal C: Particles and Fields, 2022)
Abstract The processes in the first order of perturbations of de Sitter quantum electrodynamics (QED) in Coulomb gauge are studied but setting our recently proposed rest frame vacuum of the Dirac field instead of the traditional adiabatic one. This vacuum gives rise to a new phenomenology favouring the transitions between neutral states, i.e. the pair creation from a photon and the lepton creation from vacuum, while the transitions between charged states are inhibited. The probabilities per unit of volume and unit of time are derived in the conformal chart according to a new definition that holds even if the energy is no longer conserved. Surprisingly, these probabilities have new logarithmic singularities apart from the poles usually arising in perturbations. These singularities affect the probabilities in the critical positions in which the fermion momenta are either parallel or anti-parallel and the helicity is conserved. To remove all these singularities, a regularization is first performed to extract the logarithmic one before removing the poles, applying the usual reduction procedure. It is shown that the resulting reduced probabilities reach their maxima only in the critical positions, thus complying with the helicity conservation. The corresponding time-dependent probabilities in the physical local chart govern a simple model of fermion creation from vacuum, $$vac→ γ +e^++e^-→ (e^++e^-)+e^++e^-$$ v a c → γ + e + + e - → ( e + + e - ) + e + + e - , which rapidly reaches saturation because of the pair creation which is dominant.