A new approach to path integral quantum mechanics in curved space-time for a scalar particle is presented in terms of local curvature involving Fermi or Riemann normal co-ordinates. This approach involves use of a local time translation operator with Lie transport that, while strictly non-unitary in form, nonetheless yields the correct expression for the curved space-time free-particle Lagrangian in the sum-over-histories, with additional terms corresponding to a curvature-dependent violation of probability. These terms simultaneously induce a breakdown of time-reversal symmetry at the quantum mechanical level, and also a violation of the weak equivalence principle at the particle's Compton wavelength scale. Furthermore, the scalar propagator generates a gravitational analogue of the Aharonov-Bohm effect and Berry's phase through the appearance of an overall gauge-invariant phase factor. Future directions to follow from this initial research are presented.
Quantum mechanics in curved space-time
