Phase space path integral in curved space

TL;DR

This paper develops a phase space path integral formulation in curved Riemannian space, using a novel prescription that treats coordinates and momenta symmetrically, resulting in a curvature coupling in the Schrödinger equation.

Contribution

It introduces a new method for constructing phase space path integrals in curved space that naturally incorporates Riemannian geometry and operator ordering effects.

Findings

Derivation of the phase space path integral in curved space.

Operator ordering leads to DeWitt curvature coupling.

Consistent treatment of coordinates and momenta in normal coordinates.

Abstract

Phase space path integral is worked out in a riemannian geometry, by employing a prescription for the infinitesimal propagator that takes riemannian normal coordinates and momenta on an equal footing. The operator ordering induced by this prescription leads to the DeWitt curvature coupling in the Schrodinger equation.