Feynman's path integral and mutually unbiased bases

Details Feynman's path integral and mutually unbiased bases Feynman's path integral and mutually unbiased bases

2009-04-06

arxiv.org/abs/0904.0886v2

J. Phys. A: Math. Theor. 42 (2009) 245306 (11 pp)

Physics

Quantum Physics

12 pages, submitted to Journal of Physics A: Math. Theor., minor corrections

Scientific paper

10.1088/1751-8113/42/24/245306

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.

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