A New Perspective on Path Integral Quantum Mechanics in Curved Space-Time
1 Department of Physics, University of Regina - Regina, Saskatchewan, S4S 0A2, Canada
2 Department of Physics and Engineering Physics, University of Saskatchewan - Saskatoon, Saskatchewan, S7N 5E2, Canada
Published online: 5 September 2013
Abstract. A new approach to path integral quantum mechanics in curved space-time is presented for scalar particle propagation, expressed in terms of Lie transport and Fermi or Riemann normal co-ordinates to describe local curvature. While the presence of local curvature results in a strictly non-unitary representation of local time translation, the formalism nevertheless correctly recovers the free-particle Lagrangian in curved space-time, along with new terms that predict a simultaneous breakdown of time-reversal symmetry and a quantum violation of the weak equivalence principle at the particle’s Compton wavelength scale. Furthermore, the formalism reveals the prediction of a gauge-invariant phase factor interpreted as the gravitational Aharonov-Bohm effect and Berry’s phase.
© Owned by the authors, published by EDP Sciences, 2013
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