Related papers: Wavelets in mathematical physics: q-oscillators
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
Using free field representation of quantum affine algebra $U_q(\widehat{sl_2})$, we investigate the structure of the Fock modules over $U_q(\widehat{sl_2})$. The analisys is based on a $q$-analog of the BRST formalism given by Bernard and…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
New algebraic structure on electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches.…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part, according to variational approach we obtain a…
Certain non-linear relations between the generators of the (q-deformed) Heisenberg algebra are found. Some of these relations are invariant under quantization and $q$-deformation.
The physical interpretation of the main notions of the quantum group theory (coproduct, representations and corepresentations, action and coaction) is discussed using the simplest examples of $q$-deformed objects (quantum group…
We solve the problem of Fourier transformation for the one-dimensional $q$-deformed Heisenberg algebra. Starting from a matrix representation of this algebra we observe that momentum and position are unbounded operators in the Hilbert…
A class of well-behaved *-representations of a q-deformed Heisenberg algebra is studied and classified.
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…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…
Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
In this paper, we propose a full characterization of a generalized $q-$deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the…
We present an application of variational-wavelet analysis to quasiclassical calculations of solutions of Wigner equations related to nonlinear (polynomial) dynamical problems. (Naive) deformation quantization, multiresolution…
It was recently discovered that waves scattering off a $Q$-ball can extract energy from it. We present an analytical treatment of this process by adopting a multi-step function approximation for the background field, which yields…
This lecture consists of two sections. In section 1 we consider the simplest version of a q-deformed Heisenberg algebra as an example of a noncommutative structure. We first derive a calculus entirely based on the algebra and then formulate…
The continuous big $q$-Hermite polynomials are shown to realize a basis for a representation space of an extended $q$-oscillator algebra. An expansion formula is algebraically derived using this model.
A method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced. Explicit results of such realizations are provided for…