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

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.