Abstract
A fundamentally different approach to path integral quantum mechanics in curved spacetime is presented for scalar particle propagation on a locally curved background, as described by Fermi or Riemann normal coordinates. While using a strictly non-unitary form of local time translation involving Lie transport, the formalism nevertheless correctly recovers the free-particle Lagrangian in curved spacetime, plus new contributions. All the probability violating terms due to curvature contribute to a quantum violation of the weak equivalence principle at the particle's Compton wavelength scale and the propagator yields a gauge-invariant phase factor interpreted as the gravitational Aharonov–Bohm effect and Berry's phase.
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