Abstract
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.
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