Path Integral Measure Via the Schwinger-Dyson Equations

Abstract

We present a way for calculating the Lagrangian path integral measure directly from the Hamiltonian Schwinger--Dyson equations. The method agrees with the usual way of deriving the measure, however it may be applied to all theories, even when the corresponding momentum integration is not Gaussian. Of particular interest is the connection that is made between the path integral measure and the measure in the corresponding 0-dimensional model. This allows us to uniquely define the path integral even for the case of Euclidean theories whose action is not bounded from below.