A Naturally Renormalized Quantum Field Theory

It was shown that quantum metric fluctuations smear out the singularities of Green functions on the light cone (Ford, ), but it does not remove other ultraviolet divergences of the quantum field theory (QFT). We have proved that quantization in indefinite metric, i.e. QFT in Krein space, removes all divergences of the theory except light cone singularity (Gazeau, et al., Class. Quantum Gravity, 17:1415, 2000, ; Takook, Int. J. Mod. Phys. E, 11:509, 2002, ). In this paper, by considering the QFT in Krein space and the quantum metric fluctuations, it is shown that all divergences can be removed.