相关论文: Comment on $q$-deformation in Second Quantization …
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…
We review several procedures of quantization formulated in the framework of (classical) phase space M. These quantization methods consider Quantum Mechanics as a "deformation" of Classical Mechanics by means of the "transformation" of the…
The quantum deformation concept is applied to a study of isovector pairing correlations in nuclei of the mass 40<A<100 region. While the non-deformed (q -> 1) limit of the theory provides a reasonable global estimate for strength parameters…
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 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 discuss quantum deformation of the affine transformation algebra. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators.
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
Two coalgebra structures are used in quantum field theory. The first one is the coalgebra part of a Hopf algebra leading to deformation quantization. The second one is a co-module co-algebra over the first Hopf algebra and it is used to…
We define a generalized $(q;\alpha,\beta,\gamma;\nu)$-deformed oscillator algebra and study the number of its characteristics. We describe the structure function of deformation, analyze the classification of irreducible representations and…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
Attention is focused on q-deformed quantum algebras with physical importance, i.e. $U_{q}(su_{2})$, $U_{q}(so_{4})$ and q-deformed Lorentz algebra. The main concern of this article is to assemble important ideas about these symmetry…
Deformations of quantum field theories which preserve Poincar\'e covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an…
We use Berezin's quantization procedure to obtain a formal $U_q su_{1,1}$-invariant deformation of the quantum disc. Explicit formulae for the associated q-bidifferential operators are produced.
An explicit realization of the W(2,2) Lie algebra is presented using the famous bosonic and fermionic oscillators in physics, which is then used to construct the q-deformation of this Lie algebra. Furthermore, the quantum group structures…
Given a real number $q$ such that $0<q<1$, the natural setting for the mathematics of a $q$-oscillator is an infinite-dimensional, separable Hilbert space that is said to provide an interpolation between the Bargmann-Segal space of…
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-parameter quantum algebra is given by using mixed perverse…
We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wavefunctions of the system.…
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…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first)- class…