A brief review on the Problem of Divergence in Krein Space Quantization

TL;DR

This paper reviews how Krein space quantization addresses divergence issues in quantum field theory, demonstrating automatic regularization and finite results in QED and Casimir effect calculations.

Contribution

It introduces Krein space quantization as a method that naturally eliminates divergences, providing finite results without traditional regularization techniques.

Findings

Krein space quantization yields finite results for QED divergences.

The method automatically regularizes infrared and ultraviolet divergences.

Finite Casimir stress calculations in de Sitter spacetime are achieved.

Abstract

In this paper we have a brief review on the problem of divergence in quantum field theory and its elimination using the method of Krein space quantization. In this method, the auxiliary negative frequency states have been utilized, the modes of which do not interact with the physical states and are not affected by the physical boundary conditions. It is remarkable that Krein space quantization is similar to Pauli-Villars regularization, so we can call it the "Krein regularization". Considering the QED in Krein space quantization, it could be shown that the theory is automatically regularized. Calculation of the three primitive divergent integrals, the vacuum polarization, electron self energy and vertex function using Krein space method leads to finite values, since the infrared and ultraviolet divergencies do not appear. For another example, the Casimir stress on a spherical shell in de Sitter spacetime for a massless scalar field could be calculated using Krein space quantization.