Hypercomplex Fock states for discrete electromagnetic Schrödinger operators: A Bayesian probability perspective

Abstract

We present and study a new class of Fock states underlying to discrete electromagnetic Schrödinger operators from a multivector calculus perspective. This naturally lead to hypercomplex versions of Poisson-Charlier polynomials, Meixner polynomials, among other ones. The foundations of this work are based on the exploitation of the quantum probability formulation 'à la Dirac' to the setting of Bayesian probabilities, on which the Fock states arise as discrete quasi-probability distributions carrying a set of independent and identically distributed (i.i.d) random variables. By employing Mellin-Barnes integrals in the complex plane we obtain counterparts for the well-known multidimensional Poisson and hypergeometric distributions, as well as quasi-probability distributions that may take negative or complex values on the lattice hZ n .

Relativistic Wave Equations on the Lattice: An Operational Perspective

“…Thus F h,α Ψ(ξ, t) is a solution of the evolution problem (21), and whence, the ansatz (41) solves the discretized Klein-Gordon equation (20).…”

Time-changed Dirac-Fokker-Planck equations on the lattice

“…For our purposes (time-changed equation depending on the Hurst parameter 0 < H < 1) it becomes relevant to consider, as in author's recent paper [11], the generalized Wright functions p Ψ q to encompass the stable one-side Lévy distributions L H (u) of order 0 < H < 1 appearing on subsection 4.2 and the Fourier multipliers cos µt d h (ξ) 2 and sin(µt…”