Feynman's path integral and mutually unbiased bases

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.

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

References in corpus (3)

• Automorphisms of the fine grading of sl(n,C) associated with the generalized Pauli matrices
• Variations on a theme of Heisenberg, Pauli and Weyl
• Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions

Cited by in corpus (10)

• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
• Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?
• Construction of mutually unbiased bases with cyclic symmetry for qubit systems
• Weak mutually unbiased bases
• Symmetries of the finite Heisenberg group for composite systems
• Symmetries of finite Heisenberg groups for multipartite systems
• An analytic function approach to weak mutually unbiased bases
• Clifford group is not a semidirect product in dimensions $N$ divisible by four
• Symmetries of finite Heisenberg groups for k-partite systems
• A classification of finite quantum kinematics