One-loop approximation of Moller scattering in Krein-space quantization

TL;DR

This paper demonstrates that using Krein space quantization in quantum field theory eliminates ultraviolet divergences in one-loop M{46}ller scattering calculations, providing a divergence-free approach.

Contribution

It introduces a method to compute M{46}ller scattering in Krein space, showing automatic removal of ultraviolet divergences at one-loop level.

Findings

Ultraviolet divergences are eliminated in the one-loop approximation.

Krein space quantization combined with quantum metric fluctuations results in divergence-free quantum field theory.

The approach simplifies calculations by avoiding traditional renormalization procedures.

Abstract

It has been shown that the negative-norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter spacetime [1,2]. In this processes ultraviolet and infrared divergences have been automatically eliminated [3]. A natural renormalization of the one-loop interacting quantum field in Minkowski spacetime ($\lambda\phi^4$) has been achieved through the consideration of the negative-norm states defined in Krein space. It has been shown that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuation, results in quantum field theory without any divergences [4]. Pursuing this approach, we express Wick's theorem and calculate M{\o}ller scattering in the one-loop approximation in Krein space. The mathematical consequence of this method is the disappearance of the ultraviolet divergence in the one-loop approximation.