Feynman's path integral and mutually unbiased bases
Quantum Physics
2009-08-05 v2
Abstract
Our previous work on quantum mechanics in Hilbert spaces of finite dimensions N is applied to elucidate the deep meaning of Feynman's path integral pointed out by G. Svetlichny. He speculated that the secret of the Feynman path integral may lie in the property of mutual unbiasedness of temporally proximal bases. We confirm the corresponding property of the short-time propagator by using a specially devised N x N -approximation of quantum mechanics in L^2(R) applied to our finite-dimensional analogue of a free quantum particle.
Keywords
Cite
@article{arxiv.0904.0886,
title = {Feynman's path integral and mutually unbiased bases},
author = {J Tolar and G Chadzitaskos},
journal= {arXiv preprint arXiv:0904.0886},
year = {2009}
}
Comments
12 pages, submitted to Journal of Physics A: Math. Theor., minor corrections