THE CONVERGENCE OF THE FEYNMAN PATH INTEGRALS IN THE WEIGHTED SOBOLEV SPACES AND ITS APPLICATION

There are many ways to give a rigorous meaning to the Feynman path integral. In my talk especially the method of the time-slicing approximation determined through broken line paths is studied. It has been proved that these time-slicing approximate integrals of the Feynman path integral in configuration space and also in phase space converge in L² space as the discretization parameter tends to zero. In my talk it is shown that these approximate integrals of the Feynman path integral and more general form of the Feynman path integral converge in some weighted Sobolev spaces as well. In addition, as an application of this convergence result in the weighted Sobolev spaces, a rigorous proof is given of the path integral representation of correlation functions and the reduction of wave functions by the measurement.