Abstract
In the present letter we give a new method to handle the sign problem. In fact we apply the central-limit theorem on the phase, which appears in the expression of the Monte Carlo after certain manipulations. Then we can use standard methods to calculate the two expressions that appear. In fact we manage to reduce real-time integration to a case similar to imaginary-time integration. The present method can be combined with other methods such as the stationary-phase Monte Carlo methods are. We apply the present theory to the path integral representation of the time displacement amplitude.