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

Author(s)

Faustino, N.

• Document type: Journal article
• Source: Applied Mathematics and Computation; v. 315, p. 531-548, DEC 15 2017.
• Web of Science Citations: 0

Abstract

We present and study a new class of Fock states underlying to discrete electromagnetic Schrodinger 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 a 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). (C) 2017 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 13/07590-8 - Applications of discrete Clifford calculus in field theories
• Grantee: Nelson José Rodrigues Faustino
• Support Opportunities: Scholarships in Brazil - Post-Doctorate