Path integrals and Voronin's theorem on the universality of the Riemann zeta function (Q1175453)

We present a new approach to the path integral in latticized quantum theories. Our method is based on Voronin's theorems on the universality of the Riemann zeta function. We obtain a formula for the partition function as a discrete sum over ``paths'' with each path labeled by an integer and given by a zeta function evaluated at a fixed set of points in the critical strip. These points are the image of the space-time lattice resulting from a simple linear mapping. A new measure appears in our sum, and its properties are extensively discussed and a method to calculate it is given. We carried out extensive checks of the method for Euclidean quantum mechanics, and compared the results with those obtained from well-established methods as well as exact results. The comparison confirms the validity of the zeta-function method and our calculation of the measure.