Related papers: Operators of the $q$-oscillator
Given a pair of normally hyperbolic operators over (possibily different) globally hyperbolic spacetimes on a given smooth manifold, the existence of a geometric isomorphism, called {\em M{\o}ller operator}, between the space of solutions is…
This article gives a brief introduction to $q$-special functions, i.e., $q$-analogues of the classical special functions. Here $q$ is a deformation parameter, usually $0<q<1$, where $q=1$ is the classical case. The main topics to be treated…
We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry…
Based on the idea of quantum groups and paragrassmann variables, we presenta generalization of supersymmetric classical mechanics with a deformation parameter $q= \exp{\frac{2 \pi i}{k}}$ dealing with the $k =3$ case. The coordinates of the…
We find certain functional identities for the Gauss q-power function of a sum of q-commuting variables. Then we use these identities to obtain two-parameter twists of the quantum affine algebra U_q (\hat{sl}_2) and of the Yangian Y(sl_2).…
We introduce a two-parameter deformation of the classical Bosonic, Fermionic, and Boltzmann Fock spaces that is a refinement of the $q$-Fock space of [BS91]. Starting with a real, separable Hilbert space $H$, we construct the $(q,t)$-Fock…
We analyse the Witten-Woronowicz's type deformations of the Lie superalgebra osp(2,2) and obtain a deformation parametrized by three independent parameters. For some of these algebras, finite dimensional representations are formulated in…
We mostly survey results concerning the $L^2$ boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.
The $q$-calculus for generic $q$ is developed and related to the deformed oscillator of parameter $q^{1/2}$. By passing with care to the limit in which $q$ is a root of unity, one uncovers the full algebraic structure of ${{\cal…
We study a way of $q$-deformation of the bi-local system, the two particle system bounded by a relativistic harmonic oscillator type of potential, from both points of view of mass spectra and the behavior of scattering amplitudes. In our…
In the present paper we describe the procedure of the Q-operators construction for the q-deformed model, described by the Lax operator, which is important to formulate the Bethe ansatz for the Sin-Gordon model. This Lax operator can also be…
Nonextensive statistical mechanics has been a source of investigation in mathematical structures such as deformed algebraic structures. In this work, we present some consequences of $q$-operations on the construction of $q$-numbers for all…
In a recent paper it was shown that if a Hamiltonian H has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT. The inner product with respect to…
In this paper we continue the study of $Q$-operators in the six-vertex model and its higher spin generalizations. In [1] we derived a new expression for the higher spin $R$-matrix associated with the affine quantum algebra…
Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant…
In the Schroedinger formulation of non-Hermitian quantum theories a positive-definite metric operator $\eta\equiv e^{-Q}$ must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent…
We give a method for obtaining states of massive particle representations of the two-parameter deformation of the Poincar\'e algebra proposed in q-alg/9601010, q-alg/9505030 and q-alg/9501026. We discuss four procedures to generate…
Quantum--mechanical operators corresponding to canonical momentum and position of a point--like particle, which follow from the quantum field theory in the general Riemannian space-time, satisfy generally to a deformation of the canonical…
Several authors have considered whether the ultrapower and the relative commutant of a C*-algebra or II_1 factor depend on the choice of the ultrafilter. We settle each of these questions, extending results of Ge-Hadwin and the first…
The notion of index is applied to analyze the phase operator problem associated with the photon. We clarify the absence of the hermitian phase operator on the basis of an index consideration. We point out an interesting analogy between the…