Related papers: A unified representation of the q-oscillator and t…
Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…
The two-parametric quantum deformation of the algebra of coordinate functions on the supergroup GL$(1| 1)$ via a contraction of GL$_{p,q}(1| 1)$ is presented. Related differential calculus on the quantum superplane is introduced.
We study scalar field theory in one space and one time dimensions on a q-deformed space with static background. We write the Lagrangian and the equation of motion and solve it to the first order in $q-1$ where $q$ is the deformation…
Deformation theory can be used to compute the cohomology of a deformed algebra with coefficients in itself from that of the original. Using the invariance of the Euler-Poincare characteristic under deformation, it is applied here to compute…
We found hermitian realizations of the position vector $\vec{r}$, the angular momentum $\vec{\Lambda}$ and the linear momentum $\vec{p}$, all behaving like vectors under the $su_q(2)$ algebra, generated by $L_0$ and $L_\pm$. They are used…
The operator algebras of a new family of relativistic geometric models of the relativistic oscillator are studied. It is shown that, generally, the operator of number of quanta and the pair of the shift operators of each model are the…
This work introduces a novel $q$-$\hbar$ deformation of the Heisenberg algebra, designed to unify and extend several existing $q$-deformed formulations. Starting from the canonical Heisenberg algebra defined by the commutation relation…
In this article we present explicit formulae for q-differentiation on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. The…
A $q$-deformed Weyl-Heisenberg algebra is used to define a deformed displacement operator giving rise to a naturally normalized nonlinear coherent states type. Robust maximally entangled deformed coherent states are studied and the effect…
The q-deformation of harmonic oscillators is shown to lead to q-nonlinear vibrations. The examples of q-nonlinearized wave equation and Schr\"odinger equation are considered. The procedure is generalized to broader class of nonlinearities…
Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to…
Based on the representation theory of the $q$-deformed Lorentz and Poincar\'e symmeties $q$-deformed relativistic wave equation are constructed. The most important cases of the Dirac-, Proca-, Rarita-Schwinger- and Maxwell- equations are…
In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…
The classical and quantum oscillator model on Lie-algebraically deformed nonrelativistic space-time is introduced and analyzed. The corresponding equations of motions are studied using mostly numerical methods. The time-dependent energy…
We present a method of a quantum simulation of a quantum harmonic oscillator in a special case of the deformed commutation relation, which corresponds to the so-called q-deformed oscillator on an IBM quantum computer. Using the method of…
We present an operator formulation of the q-deformed dual string model amplitude using an infinite set of q-harmonic oscillators. The formalism attains the crossing symmetry and factorization and allows to express the general n-point…
The aim of Part II of this paper is to try to describe wave functions on q-deformed versions of position and momentum space. This task is done within the framework developed in Part I of the paper. In order to make Part II self-contained…
(2+2)-dimensional quantum mechanical q-phase space which is the semi-direct product of the quantum plane E_q(2)/U(1) and its dual algebra e_q(2)/u(1) is constructed. Commutation and the resulting uncertainty relations are studied. ``Quantum…
A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We show that the field operators obey q-commutation relations with q…
An approach for $q$-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov…