EPJ Web of Conferences
Volume 58, 2013TM 2012 – The Time Machine Factory [unspeakable, speakable] on Time Travel in Turin
|Number of page(s)||6|
|Section||Causality in Physics|
|Published online||05 September 2013|
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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