Time evolutions in Quantum mechanics and (Lorentzian) geometry
数学物理
2016-09-07 v1 math.MP
摘要
As R.Feynman has shown to F. Dyson -- who published it then in 1990 under the name of "Feynman's proof of Maxwell's equations" -- the only interactions compatible with the canonical uncertainty relation (for scalar particles on flat ) are the Lorentz covariant electromagnetic interactions. We generalize Feynman's argument to arbitrary configuration spaces, thereby clarifying its hidden assumptions as well as its geometrical significance. In addition, our result establishes a correspondence between globally hyperbolic spacetimes and solutions to our (algebraically formulated) axioms for nonrelativistic quantum mechanics.
引用
@article{arxiv.math-ph/0301040,
title = {Time evolutions in Quantum mechanics and (Lorentzian) geometry},
author = {Mario Paschke},
journal= {arXiv preprint arXiv:math-ph/0301040},
year = {2016}
}