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 $h{\mathbb{Z}}^n$.

28 pages; Section 2. on the previous version (v3) was reformulated; subsequent sections were readjusted; title has slightly changed

References in corpus (6)

• Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
• Exact Isospectral Pairs of PT-Symmetric Hamiltonians
• Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit
• Fock Spaces, Landau Operators and the Regular Solutions of time-harmonic Maxwell equations
• Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle
• Spectrum and eigenfunctions of the lattice hyperbolic Ruijsenaars-Schneider system with exponential Morse term

Cited by in corpus (1)

• Relativistic Wave Equations on the lattice: an operational perspective