Casimir effect in Krein space quantization

Abstract

An explicit calculation of Casimir effect through an alternative approach of field quantization [1,2], has been presented in this paper. In this method, the auxiliary negative norm states have been utilized, the modes of which do not interact with the physical states or real physical world. Naturally these modes cannot be affected by the physical boundary conditions. Presence of negative norm states play the rule of an automatic renormalization device for the theory.

Power Spectrum in Krein Space Quantization

“…In the gauge QFT, the auxiliary negative norm states (ghost states), can neither propagate in the physical world nor interact with physical states. In the previous works, we have shown that presence of negative norm states play the role of an automatic renormalization device for certain problems [5,7,14,15,17,19,20].…”

A Naturally Renormalized Quantum Field Theory

“…One of the interesting results of this construction is that the quantum field theory in Krein space removes all ultraviolet divergences of quantum field theory with exception of the light cone singularity. In the previous works, we had shown that presence of negative norm states play the role of an automatic renormalization device for certain problems [2,3,8,9,10,11,12].…”

Gupta-Bleuler quantization for massive and massless free vector fields

“…It has been shown that these auxiliary states automatically renormalize the infrared divergence in the two-point function [3,4] and remove the ultraviolet divergence in the vacuum energy [2]. This method is applied to the massless vector field in de Sitter space [8,9], interacting quantum fields and Casimir effect in Mincowski space-time [10][11][12].…”

“…This new quantization method is used for consideration of the Casimir effect for the scalar field [10]. It can be extended for the electromagnetic field in 4-dimensional spacetime.…”