Natural Renormalized One-loop Effective Action for the scalar field in a curved space-time

In previous paper [1] was shown that the negative norm states appear in a covariant quantization of the minimally coupled scalar field in de Sitter space, which eliminates any infrared divergence. Then we generalized this method to the intraction quantum field in the Minkowski space ($\lambda\phi^4$ theory), which gave an natural renormalisation procedure [2]. In this paper we would like to use this method for calculating the one-loop effective action for scalar field in a general curved space-time. It is found that any divergence would not appear and there is not need to change the Einstein's field equation for divergence elimination. This result is very important in quantum gravity