Related papers: q-oscillators, (non-)Kaehler manifolds and constra…
Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the $q$-- and the $qp$--deformed algebras arise as special cases are studied. Quantum and classical models for the corresponding…
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,…
A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra. Therefore, these operators are not Hermitian, nor is the Hamiltonian operator built from them. In the…
The subject of this study is Quantum and Statistical Mechanics of the Early Universe. In it a new approach to investigation of these two theories - density matrix deformation - is proposed. The distinguishing feature of the proposed…
Different analogs of quasiclassical limit for a q-oscillator which result in different (commutative and non-commutative) algebras of ``classical'' observables are derived. In particular, this gives the q-deformed Poisson brackets in terms…
Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. For the fractional harmonic oscillator, the corresponding q-number is derived.…
The quantum deformation of the oscillator algebra and its implications on the phase operator are studied from a view point of an index theorem by using an explicit matrix representation. For a positive deformation parameter $q$ or…
In this paper the q-deformed $W$ algebra $\WW_q$ is constructed, whose nontrivial quantum group structure is presented.
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting…
The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…
In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…
A difference operator realization of quantum deformed oscillator algebra $H_q(1)$ with a Casimir operator freedom is introduced. We show that this $H_q(1)$ have a nonlinear mapping to the deformed quantum su(2) which was introduced by…
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or $q$-boson algebra which…
A new 2-parameter quadratic deformation of the quantum oscillator algebra and its 1-parameter deformed Heisenberg subalgebra are considered. An infinite dimensional Fock module representation is presented which at roots of unity contains…
In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the…
We discuss the alternative algebraic structures on the manifold of quantum states arising from alternative Hermitian structures associated with quantum bi-Hamiltonian systems. We also consider the consequences at the level of the Heisenberg…
We study the canonical quantization of the damped harmonic oscillator by resorting to the realization of the q-deformation of the Weyl-Heisenberg algebra (q-WH) in terms of finite difference operators. We relate the damped oscillator…
We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be…
The intimate connection between q-deformed Heisenberg uncertainty relation and the Jackson derivative based on q-basic numbers has been noted in the literature. The purpose of this work is to establish this connection in a clear and…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…