Vacuum polarization of weak interaction theory in Krein space quantization

In this paper, one of the most important diagrams of weak interaction (vacuum polarization) is studied in Krein space quantization (KSQ). This diagram has divergent terms in Hilbert space which must be eliminated using a traditional regularization method like dimensional regularization whereas in KSQ the result is automatically finite and does not need renormalization.

Effective action of in Krein space quantization

The appearance of divergence creates computational issues in the process of calculating the one-loop effective action of [Formula: see text] in quantum field theory. In this paper, it is demonstrated that using Krein space quantization with Ford’s method of fluctuated metrics, divergence can be removed and that without using any traditional regularization method, it is possible to arrive at a finite solution for the effective action.

Krein Space Quantization of Casimir Effect for a Spherical Shell

The Casimir stress on a spherical shell in de Sitter spacetime for a massless scalar field is calculated using 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. These unphysical states just play the role of an automatic renormalization tool for the theory.

THE ONE-LOOP APPROXIMATION OF THE TRANSITION AMPLITUDE IN KREIN SPACE QUANTIZATION

An explicit calculation of the transition amplitude in the one-loop approximation in Krein space quantization, has been presented in this paper. As we know the loop integrals in the Feynman diagrams will be often diverged, so it is needed to introduce a regulator (Renormalization condition). In Ref. 1 the λϕ4 theory in Krein space has been considered, it has been proved that the disappearance of the ultraviolet divergence to the one-loop approximation is the direct result of Krein space quantization method. Here it is shown that the transition amplitude in the one-loop approximation in Krein space is finite, and its quantity has been calculated. So the theory is automatically regularized.