Related papers: Star products and deformed oscillators
We develop a star-product scheme of symbols defined by the normally ordered powers of the creation and annihilation photon operators, (a\dag)^m a^n. The corresponding phase space is a two-dimensional lattice with nodes (m,n) given by pairs…
We investigate a quantum mechanical harmonic oscillator based on the extended Snyder model. This realization of the Snyder model is constructed as a quantum phase space generated by $D$ spatial coordinates and $D(D-1)/2$ tensorial degrees…
We study the general form of the noncommutative associative product (the star-product) on the Grassman algebra; the star-product is treated as a deformation of the usual "pointwise" product. We show that up to a similarity transformation,…
Starting from noncommutative generalization of Minkowski space we consider quantum deformed relativistic symmetries which lead to the modification of kinematics of special relativity. The noncommutative field theory framework described by…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
Harmonic oscillator in Fock space is defined. Isospectral as well as polynomiality-of-eigenfunctions preserving, translation-invariant discretization of the harmonic oscillator is presented. Dilatation-invariant and…
We review some aspects of the relation between ordinary coherent states and q-deformed generalized coherent states with some of the simplest cases of quantum Lie algebras. In particular, new properties of (q-)coherent states are utilized to…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
This set of notes corresponds to a mini-course given in September 2018 in Bedlewo; it does not contain any new result; it complements -- with intersection -- the introduction to formal deformation quantization and group actions,…
The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a…
We investigate noncommutative deformations of quantum field theories for different star products, particularly emphasizing the locality properties and the regularity of the deformed fields. Using functional analysis methods, we describe the…
The dynamics of hybrid systems -- i.e. ones in which classical and quantum degrees of freedom co-exist and interact -- feature both diffusion in the classical sector and decoherence in the quantum state. In this article, we will consider…
The coherent states for twist-deformed oscillator model provided in article [1] are constructed. Besides, it is demonstrated that the energy spectrum of considered model is labeled by two quantum numbers - by so-called main and azimutal…
We present a classification of homogeneous star products on duals of Lie algebroids in terms of the second Lie algebroid cohomology. Moreover, we extend this classification to projectable star products, i.e., to quantizations compatible…
We transform the oscillator algebra with kappa-deformed multiplication rule, proposed in [1],[2], into the oscillator algebra with kappa-deformed flip operator and standard multiplication. We recall that the kappa-multiplication of the…
Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space…
Given a star product with separation of variables on a pseudo-Kaehler manifold, we obtain a new formal (1,1)-form from its classifying form and call it the phase form of the star product. The cohomology class of a star product with…
Invertible maps from operators of quantum obvservables onto functions of c-number arguments and their associative products are first assessed. Different types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution are…
Based on the nonperturbative analysis, we show that the classical motion of harmonic oscillator derived from the deformed QM is manifestly in contradiction with observations. For this reason, we take an alternate way for estimating the…
Some physical systems like the quantum mechanics with magnetic charges or field theoretical models appearing in the context of string theory are formulated in terms of non-associative algebras. Hence, demand non-associative star products…