Coherent state quantization of paragrassmann algebras

By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators leads to interesting conclusions.

Quantum current algebra for the AdS(5) x S(5) superstring

The sigma model describing the dynamics of the superstring in the AdS(5) x S(5) background can be constructed using the coset PSU(2, 2 vertical bar 4)/SO(4, 1) x SO(5). A basic set of operators in this two dimensional conformal field theory is composed by the left invariant currents. Since these currents are not (anti) holomorphic, their OPE`s is not determined by symmetry principles and its computation should be performed perturbatively. Using the pure spinor sigma model for this background, we compute the one-loop correction to these OPE`s. We also compute the OPE`s of the left invariant currents with the energy momentum tensor at tree level and one loop.

Influence of interlayer tunneling on the quantized Hall phases in intentionally disordered multilayer structures

Stability of the quantized Hall phases is studied in weakly coupled multilayers as a function of the interlayer correlations controlled by the interlayer tunneling and by the random variation of the well thicknesses. A strong enough interlayer disorder destroys the symmetry responsible for the quantization of the Hall conductivity, resulting in the breakdown of the quantum Hall effect. A clear difference between the dimensionalities of the metallic and insulating quantum Hall phases is demonstrated. The sharpness of the quantized Hall steps obtained in the coupled multilayers with different degrees of randomization was found consistent with the calculated interlayer tunneling energies. The observed width of the transition between the quantized Hall states in random multilayers is explained in terms of the local fluctuations of the electron density.

Compressibility of electron liquid in the quantized Hall phase of GaAs/AlGaAs multi-layers

Magneto-capacitance was studied in narrow miniband GaAs/AlGaAs superlattices where quasi-two dimensional electrons revealed the integer quantum Hall effect. The interwell tunneling was shown to reduce the effect of the quantization of the density of states on the capacitance of the superlattices. In such case the minimum of the capacitance observed at the filling factor nu = 2 was attributed to the decrease of the electron compressibility due to the formation of the incompressible quantized Hall phase. In accord with the theory this phase was found strongly inhomogeneous. The incompressible fraction of the quantized Hall phase was demonstrated to rapidly disappear with the increasing temperature. (C) 2008 Elsevier B.V. All rights reserved.

Linear covariant gauges on the lattice

Linear covariant gauges, such as Feynman gauge, are very useful in perturbative calculations. Their non-perturbative formulation is, however, highly non-trivial. In particular, it is a challenge to define linear covariant gauges on a lattice. We consider a class of gauges in lattice gauge theory that coincides with the perturbative definition of linear covariant gauges in the formal continuum limit. The corresponding gauge-fixing procedure is described and analyzed in detail, with an application to the pure SU(2) case. In addition, results for the gluon propagator in the two-dimensional case are given. (C) 2008 Elsevier B.V. All rights reserved.

On high Q(2) behavior of the pion form factor for transitions gamma*gamma -> pi(0) and gamma*gamma* -> pi(0) within the nonlocal quark-pion model

The behavior of the transition pion form factor for processes gamma (*)gamma --> pi(0) and gamma (*)gamma (*) --> pi(0) at large values of space-like photon momenta is estimated within the nonlocal covariant quark-pion model. It is shown that, in general, the coefficient of the leading asymptotic term depends dynamically on the ratio of the constituent quark mass and the average virtuality of quarks in the vacuum and kinematically on the ratio of photon virtualities. The kinematic dependence of the transition form factor allows us to obtain the relation between the pion light-cone distribution amplitude and the quark-pion vertex function. The dynamic dependence indicates that the transition form factor gamma (*)gamma -->, pi(0) at high momentum transfers is very sensitive to the nonlocality size of nonperturbative fluctuations in the QCD vacuum. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Electric charge quantization and the muon anomalous magnetic moment

We investigate some proposals to solve the electric charge quantization puzzle that simultaneously explain the recent measured deviation on the muon anomalous magnetic moment. For this we assess extensions of the electro-weak standard model spanning modifications on the scalar sector only. It is interesting to verify that one can have modest extensions which easily account for the solution for both problems.

Asymptotic soliton train solutions of the defocusing nonlinear Schrodinger equation

Asymptotic behavior of initially large and smooth pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrodinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Then, asymptotic soliton trains arising eventually from a large and smooth initial pulse are studied by means of a semiclassical method. The parameter varying along the soliton train is calculated from the generalized Bohr-Sommerfeld quantization rule, so that the distribution of eigenvalues depends on two functions-intensity rho(0)(x) of the initial pulse and its initial chirp v(0)(x). The influence of the initial chirp on the asymptotic state is investigated. Excellent agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.

Towards a worldsheet derivation of the Maldacena conjecture

A U(2,2 vertical bar 4)-invariant A-model constructed from fermionic superfields has recently been proposed as a sigma model for the superstring on AdS(5) X S(5). After explaining the relation of this A-model with the pure spinor formalism, the A-model action is expressed as a gauged linear sigma model. In the zero radius limit, the Coulomb branch of this sigma model is interpreted as D-brane holes which are related to gauge-invariant N = 4 d=4 super-Yang-Mills operators. As in the worldsheet derivation of open-closed duality for Chem-Simons theory, this construction may lead to a worldsheet derivation of the Maldacena conjecture. Intriguing connections to the twistorial formulation of N = 4 Yang-Mills are also noted. (Republished with permission of JHEP from JHEP 0803:031, 2008.)

Explaining the pure spinor formalism for the superstring

After adding a pair of non-minimal fields and performing a similarity transformation, the BRST operator in the pure spinor formalism is expressed as a conventional-looking BRST operator involving the Virasoro constraint and (b, c) ghosts, together with 12 fermionic constraints. This BRST operator can be obtained by gauge-fixing the Green-Schwarz superstring where the 8 first-class and 8 second-class Green-Schwarz constraints are combined into 12 first-class constraints. Alternatively, the pure spinor BRST operator can be obtained from the RNS formalism by twisting the ten spin-half RNS fermions into five spin-one and five spin-zero fermions, and using the SO(10)/U(5) pure spinor variables to parameterize the different ways of twisting. GSO(-) vertex operators in the pure spinor formalism are constructed using spin fields and picture-changing operators in a manner analogous to Ramond vertex operators in the RNS formalism.

Integrability vs supersymmetry: Poisson structures of the pohlmeyer reduction

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stochastic quantization of real-time thermal field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Financial comparisons of the artisanal fisheries in Urubupungá Complex in the middle Paraná River (Brazil)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Quantization of (2+1)-spinning particles and bifermionic constraint problem

This work is a natural continuation of our recent study in quantizing relativistic particles. There it was demonstrated that, by applying a consistent quantization scheme to the classical model of a spinless relativistic particle as well as to the Berezin-Marinov model of a 3 + 1 Dirac particle, it is possible to obtain a consistent relativistic quantum mechanics of such particles. In the present paper, we apply a similar approach to the problem of quantizing the massive 2 + 1 Dirac particle. However, we stress that such a problem differs in a nontrivial way from the one in 3 + 1 dimensions. The point is that in 2 + 1 dimensions each spin polarization describes different fermion species. Technically this fact manifests itself through the presence of a bifermionic constant and of a bifermionic first-class constraint. In particular, this constraint does not admit a conjugate gauge condition at the classical level. The quantization problem in 2 + 1 dimensions is also interesting from the physical viewpoint (e.g., anyons). In order to quantize the model, we first derive a classical formulation in an effective phase space, restricted by constraints and gauges. Then the condition of preservation of the classical symmetries allows us to realize the operator algebra in an unambiguous way and construct an appropriate Hilbert space. The physical sector of the constructed quantum mechanics contains spin-1/2 particles and antiparticles without an infinite number of negative-energy levels, and exactly reproduces the one-particle sector of the 2 + 1 quantum theory of a spinor field.

Comments on spin operators and spin-polarization states of 2+1 fermions

In this brief article we discuss spin-polarization operators and spin-polarization states of 2 + 1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the use of such a representation allows us to introduce the conserved covariant spin operator in the 2 + 1 field theory. Another advantage of this representation is related to the pseudoclassical limit of the theory. Indeed, quantization of the pseudoclassical model of a spinning particle in 2 + 1 dimensions leads to the 4-spinor representation as the adequate realization of the operator algebra, where the corresponding operator of a first-class constraint, which cannot be gauged out by imposing the gauge condition, is just the covariant operator previously introduced in the quantum theory.