XXVIII Workshop on Geometric Methods in Physics 28.06-04.07.2009

Goce Chadzitaskos

Feynman's path integral and mutually unbiased bases

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. 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.