32 research outputs found
Obstruction Results in Quantization Theory
We define the quantization structures for Poisson algebras necessary to
generalise Groenewold and Van Hove's result that there is no consistent
quantization for the Poisson algebra of Euclidean phase space. Recently a
similar obstruction was obtained for the sphere, though surprising enough there
is no obstruction to the quantization of the torus. In this paper we want to
analyze the circumstances under which such obstructions appear. In this context
we review the known results for the Poisson algebras of Euclidean space, the
sphere and the torus.Comment: 34 pages, Latex. To appear in J. Nonlinear Scienc
Three dimensional quadratic algebras: Some realizations and representations
Four classes of three dimensional quadratic algebras of the type \lsb Q_0 ,
Q_\pm \rsb , \lsb Q_+ , Q_- \rsb ,
where are constants or central elements of the algebra, are
constructed using a generalization of the well known two-mode bosonic
realizations of and . The resulting matrix representations and
single variable differential operator realizations are obtained. Some remarks
on the mathematical and physical relevance of such algebras are given.Comment: LaTeX2e, 23 pages, to appear in J. Phys. A: Math. Ge
New q-deformed coherent states with an explicitly known resolution of unity
We construct a new family of q-deformed coherent states , where . These states are normalizable on the whole complex plane and continuous
in their label . They allow the resolution of unity in the form of an
ordinary integral with a positive weight function obtained through the analytic
solution of the associated Stieltjes power-moment problem and expressed in
terms of one of the two Jacksons's -exponentials. They also permit exact
evaluation of matrix elements of physically-relevant operators. We use this to
show that the photon number statistics for the states is sub-Poissonian and
that they exhibit quadrature squeezing as well as an enhanced signal-to-quantum
noise ratio over the conventional coherent state value. Finally, we establish
that they are the eigenstates of some deformed boson annihilation operator and
study some of their characteristics in deformed quantum optics.Comment: LaTeX, 26 pages, contains 9 eps figure
Deformed oscillator algebras for two dimensional quantum superintegrable systems
Quantum superintegrable systems in two dimensions are obtained from their
classical counterparts, the quantum integrals of motion being obtained from the
corresponding classical integrals by a symmetrization procedure. For each
quantum superintegrable systema deformed oscillator algebra, characterized by a
structure function specific for each system, is constructed, the generators of
the algebra being functions of the quantum integrals of motion. The energy
eigenvalues corresponding to a state with finite dimensional degeneracy can
then be obtained in an economical way from solving a system of two equations
satisfied by the structure function, the results being in agreement to the ones
obtained from the solution of the relevant Schrodinger equation. The method
shows how quantum algebraic techniques can simplify the study of quantum
superintegrable systems, especially in two dimensions.Comment: 22 pages, THES-TP 10/93, hep-the/yymmnn