Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

QUASIDISTRIBUTIONS and COHERENT STATES FOR FINITE-DIMENSIONAL QUANTUM SYSTEMS

In recent years, an approach to discrete quantum phase spaces which comprehends all the main quasiprobability distributions known has been developed. It is the research that started with the pioneering work of Galetti and Piza, where the idea of operator bases constructed of discrete Fourier transforms of unitary displacement operators was first introduced. Subsequently, the discrete coherent states were introduced, and finally, the s-parametrized distributions, that include the Wigner, Husimi, and Glauber-Sudarshan distribution functions as particular cases. In the present work, we adapt its formulation to encompass some additional discrete symmetries, achieving an elegant yet physically sound formalism.

Scalar quantum field theory in disordered media

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dressing approach to the nonvanishing boundary value problem for the AKNS hierarchy

We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solutions are found by introducing appropriate vertex operators that takes into account the boundary conditions.

New class of spin projection operators for 3D models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An algebraic q-deformed form for shape-invariant systems

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show that these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserves the shape-invariance property presented by the primary system. q-deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.

Field-theory Two-point Functions via Negative Dimension Integration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Vertex operators and Jordan fields

The construction of Lie algebras in terms of Jordan algebra generators is discussed. The key to the construction is the triality relation already incorporated into matrix products. A generalisation to Kac-Moody algebras in terms of vertex operators is proposed and may provide a clue for the construction of new representations of Kac-Moody algebras in terms of Jordan fields. © 1988.

On the structure of quantum phase space

The space of labels characterizing the elements of Schwinger's basis for unitary quantum operators is endowed with a structure of symplectic type. This structure is embodied in a certain algebraic cocycle, whose main features are inherited by the symplectic form of classical phase space. In consequence, the label space may be taken as the quantum phase space: It plays, in the quantum case, the same role played by phase space in classical mechanics, some differences coming inevitably from its nonlinear character. © 1990 American Institute of Physics.

New phenomenon of nonlinear Regge trajectory and quantum dual string theory

The relation between the spin and the mass of an infinite number of particles in a q-deformed dual string theory is studied. For the deformation parameter q a root of unity, in addition to the relation of such values of q with the rational conformal field theory, the Fock space of each oscillator mode in the Fubini-Veneziano operator formulation becomes truncated. Thus, based on general physical grounds, the resulting spin-(mass)2 relation is expected to be below the usual linear trajectory. For such specific values of q, we find that the linear Regge trajectory turns into a square-root trajectory as the mass increases.

Consistent higher derivative quantum field theory: A model without tachyons and ghosts

We present a higher derivative gauge theory in (2 + 1) dimensions which can have its parameters suitably tuned in order to become a consistent quantum field theory, in the sense that both tachyons and ghosts are absent from the particle spectrum of the theory.

Extra dimensions in superstring theory

It was earlier shown that an SO(9,1) θα spinor variable can be constructed from RNS matter and ghost fields. θα has a bosonic world-sheet super-partner λα which plays the role of a twistor variable, satisfying λΓμ λ = ∂xμ + iθΓμ ∂θ. For Type IIA superstrings, the left-moving [θL α, λL α] and right-moving [θRα, λRα] can be combined into 32-component SO(10,1) spinors [θA, λA]. This suggests that λAΓAB 11 λB = 2λL αλRα can be interpreted as momentum in the eleventh direction. Evidence for this interpretation comes from the zero-momentum vertex operators of the Type IIA superstring and from consideration of DD-branes. As in the work of Bars, one finds an SO(10,2) structure for the Type IIA superstring and an SO(9, 1) × SO(2, 1) structure for the Type IIB superstring. © 1997 Elsevier Science B.V.

Two definitions of the electric polarizability of a bound system in relativistic quantum theory

For the electric polarizability of a bound system in relativistic quantum theory, there are two definitions that have appeared in the literature. They differ depending on whether or not the vacuum background is included in the system. A recent confusion in this connection is clarified. © 1999 American Associations of Physics Teachers.