Negative Norm States in de Sitter Space and QFT without Renormalization Procedure

TL;DR

This paper explores a method involving negative norm states in quantum field theory that eliminates ultraviolet divergences, demonstrated through a $bb$ theory in Minkowski space, suggesting an automatic renormalization approach.

Contribution

It extends the use of negative norm states from de Sitter space to Minkowski space, enabling automatic renormalization of interacting quantum fields at one-loop level.

Findings

Ultraviolet divergence disappears at one-loop approximation.

Negative norm states facilitate automatic renormalization.

Method preserves physical content while removing divergences.

Abstract

In recent papers [1,2], it has been shown that the presence of negative norm states or negative frequency solutions are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content of the theory, offers the advantage of eliminating any ultraviolet divergence in the vacuum energy [2] and infrared divergence in the two point function [3]. We attempt here to extend this method to the interacting quantum field in Minkowski space-time. As an illustration of the procedure, we consider the $\lambda\phi^4$ theory in Minkowski space-time. The mathematical consequences of this method is the disappearance of the ultraviolet divergence to the one-loop approximation. This means, the effect of these auxiliary negative norm states is to allow an automatic renormalization of the theory in this approximation.