  We present and study a new class of Fock states underlying to discrete
electromagnetic Schr\"odinger 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 $h\mathbb{Z}^n$.
