A Naturally Renormalized Quantum Field Theory

TL;DR

This paper demonstrates that combining quantum field theory in Krein space with quantum metric fluctuations results in a divergence-free quantum field theory, addressing longstanding ultraviolet divergence issues.

Contribution

It introduces a novel approach that merges Krein space quantization with quantum metric fluctuations to eliminate all divergences in quantum field theory.

Findings

All divergences are removed except light cone singularity.

Quantum metric fluctuations smear out Green's function singularities.

The combined approach yields a divergence-free quantum field theory.

Abstract

It was shown that quantum metric fluctuations smear out the singularities of Green's functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, {\it i.e.} indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2,3]. In this paper, it is discussed that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuations, results in quantum field theory without any divergences.