Scalar effective action in Krein space quantization

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.