Path Integral Measure Via the Schwinger-Dyson Equations

TL;DR

This paper introduces a novel method to compute the Lagrangian path integral measure directly from Hamiltonian Schwinger-Dyson equations, applicable to a wide range of theories including non-Gaussian and unbounded Euclidean actions.

Contribution

It provides a new approach to determine the path integral measure from Hamiltonian equations, extending applicability beyond traditional Gaussian cases.

Findings

Method agrees with traditional measure derivation

Applicable to non-Gaussian and unbounded Euclidean theories

Connects path integral measure with 0-dimensional model measure

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.