Scalar effective action in Krein space quantization

TL;DR

This paper calculates the one-loop effective action for a scalar field using Krein space quantization, demonstrating its natural finiteness and comparing results with traditional methods.

Contribution

It introduces Krein space quantization for scalar fields, showing it yields finite effective actions and consistent beta-functions with standard approaches.

Findings

Effective action is finite without divergences

Beta-function matches traditional Hilbert space results

Krein space quantization alters the effective potential shape

Abstract

In this paper, the \lambda\phi^4 scalar feld effective action, in the one-loop approximation, is calculated by using the Krein space quantization. We show that the effective action is naturally fnite and the singularity does not appear in the theory. The physical interaction mass, the running coupling constant and \beta-function are then calculated. The effective potential which is calculated in the Krein space quantization is different from the usual Hilbert space calculation, however we show that \beta-function is the same in the two different methods.