A new perspective on path integral quantum mechanics in curved space–time

Abstract

We present a new approach to path integral quantum mechanics in curved space–time for a scalar particle, expressed in terms of local curvature described by Fermi or Riemann normal coordinates. This approach correctly recovers the curved space–time free-particle Lagrangian, along with new terms that reveal a simultaneous breakdown of time-reversal symmetry and the weak equivalence principle at the particle's Compton wavelength scale. The formalism reveals a further prediction of a gravitational analogue of the Aharonov–Bohm effect and Berry's phase.