2017/09/30 by Gabriel Herczeg, Andrew Waldron
Physics and Astronomy · Mathematics · #hep-th #gr-qc #math-ph #math.DG #math.MP #quant-ph
paper · pdf · doi:10.1016/j.physletb.2018.04.008
published as Physics Letters B, Volume 781, p. 312-315, 2018 · 7 pages, 1 figure, LaTeX, references added, journal version
arxiv created 2018/05/29 · arxiv updated 2018/05/31
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics.