Related papers: The Poincare lemma, antiexact forms, and fermionic…
A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…
In this paper, we develop the quantum theory of particles that has discrete Poincar\'{e} symmetry on the one-dimensional Bravais lattice. We review the recently discovered discrete Lorentz symmetry, which is the unique Lorentz symmetry that…
A representation theory of the quantized Poincar\'e ($\kappa$-Poincar\'e) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the non-deformed Poincar\'e algebra. A…
The Moyal product is used to cast the equation for the metric of a non-hermitian Hamiltonian in the form of a differential equation. For Hamiltonians of the form $p^2+V(ix)$ with $V$ polynomial this is an exact equation. Solving this…
A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally,…
In a quantum system with d-dimensional Hilbert space, the Q-function of a Hermitian positive semidefinite operator ?, is defined in terms of the d2 coherent states in this system. The Choquet integral CQ of the Q-function, is introduced…
The Heisenberg Oscillator Algebra admits irreducible representations both on the ring $B$ of polynomials in infinitely many indeterminates (the {\em bosonic representation}) and on a graded-by-{\em charge} vector space, the {\em…
We study the partially asymmetric exclusion process with open boundaries. We generalise the matrix approach previously used to solve the special case of total asymmetry and derive exact expressions for the partition sum and currents valid…
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and…
In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol…
For any orthogonal polynomials system on real line we construct an appropriate oscillator algebra such that the polynomials make up the eigenfunctions system of the oscillator hamiltonian. The general scheme is divided into two types: a…
We show that this problem gives rise to the same differential equation of a well known potential of ordinary quantum mechanics. However there is a subtle difference in the choice of the parameters of the hypergeometric function solving the…
Several issues concerning quantum kappa-Poincare algebra are discussed and reconsidered here. We propose two different formulations of kappa-Poincare quantum algebra. Firstly we present a complete Hopf algebra formulae of kappa-Poincare in…
In this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular,…
We consider a class of (possibly nondiagonalizable) pseudo-Hermitian operators with discrete spectrum, showing that in no case (unless they are diagonalizable and have a real spectrum) they are Hermitian with respect to a semidefinite inner…
Second degree polynomial Heisenberg algebras are realized through the harmonic oscillator Hamiltonian, together with two deformed ladder operators chosen as the third powers of the standard annihilation and creation operators. The…
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…
We give an extension of Pizzetti's formula associated with the Dunkl operators. It gives an explicit formula for the Dunkl inner product of an arbitrary function and a homogeneous Dunkl harmonic polynomial on the unit sphere.
We study an abstract equation in a reflexive Banach space, depending on a real parameter $\lambda$. The equation is composed by homogeneous potential operators. By analyzing the Nehari sets, we prove a bifurcation result. In some particular…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…