CONSTRUCTING QUANTUM OBSERVABLES AND SELF-ADJOINT EXTENSIONS OF SYMMETRIC OPERATORS. III. SELF-ADJOINT BOUNDARY CONDITIONS

This paper completes the review of the theory of self-adjoint extensions of symmetric operators for physicists as a basis for constructing quantum-mechanical observables. It contains a comparative presentation of the well-known methods and a newly proposed method for constructing ordinary self-adjoint differential operators associated with self-adjoint differential expressions in terms of self-adjoint boundary conditions. The new method has the advantage that it does not require explicitly evaluating deficient subspaces and deficiency indices (these latter are determined in passing) and that boundary conditions are of explicit character irrespective of the singularity of a differential expression. General assertions and constructions are illustrated by examples of well-known quantum-mechanical operators like momentum and Hamiltonian.

A user guide to simple monitoring and sustainable operation of PV-diesel hybrid systems : Handbook for system users and operators

This report contains a suggestion for a simple monitoring and evaluation guideline for PV-diesel hybrid systems. It offers system users a way to better understand if their system is operated in a way that will make it last for a long time. It also gives suggestions on how to act if there are signs of unfavourable use or failure. The application of the guide requires little technical equipment, but daily manual measurements. For the most part, it can be managed by pen and paper, by people with no earlier experience of power systems.The guide is structured and expressed in a way that targets PV-diesel hybrid system users with no, or limited, earlier experience of power engineering. It is less detailed in terms of motivations for certain choices and limitations, but rich in details concerning calculations, evaluation procedures and maintenance routines. A more scientific description of the guide can be found in a related journal article.

On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Position-dependent effective mass Dirac equations with PT-symmetric and non-PT-symmetric potentials

We present a new procedure to construct the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the context of the position-dependent effective mass Dirac equation with the vector-coupling scheme in 1 + 1 dimensions. In the first example, we consider a case for which the mass distribution combines linear and inversely linear forms, the Dirac problem with a PT-symmetric potential is mapped into the exactly solvable Schrodinger-like equation problem with the isotonic oscillator by using the local scaling of the wavefunction. In the second example, we take a mass distribution with smooth step shape, the Dirac problem with a non-PT-symmetric imaginary potential is mapped into the exactly solvable Schrodinger-like equation problem with the Rosen-Morse potential. The real relativistic energy levels and corresponding wavefunctions for the bound states are obtained in terms of the supersymmetric quantum mechanics approach and the function analysis method.

The Jacobi identity for Dirac-like brackets

For redundant second-class constraints the Dirac brackets cannot be defined and new brackets must be introduced. We prove here that the Jacobi identity for the new brackets must hold on the surface of the second-class constraints. In order to illustrate our proof we work out explicitly the cases of a fractional spin particle in 2 + 1 dimensions and the original Brink-Schwarz massless superparticle in D = 10 dimensions in a Lorentz-covariant constraints separation.

Dirac-like monopoles in three dimensions and their possible influences on the dynamics of particles

Dirac-like monopoles are studied in three-dimensional Abelian Maxwell and Maxwell-Chern-Simons models. Their scalar nature is highlighted and discussed through a dimensional reduction of four-dimensional electrodynamics with electric and magnetic sources. Some general properties and similarities whether considered in Minkowski or Euclidean space are mentioned. However, by virtue of the structure of the space-time in which they are studied, a number of differences among them occur. Furthermore, we pay attention to some consequences of these objects when they act upon the usual particles. Among other subjects, special attention is given to the study of a Lorentz-violating nonminimal coupling between neutral fermions and the field generated by a monopole alone. In addition, an analogue of the Aharonov-Casher effect is discussed in this framework.

Exact closed-form solutions of the Dirac equation for a class of effective Morse potentials

Exact bounded solutions for a fermion subject to exponential scalar potential in 1 + 1 dimensions are found in closed form. We discuss the existence of zero modes which are related to the ultrarelativistic limit of the Dirac equation and are responsible for the induction of a fractional fermion number on the vacuum.

Spin and pseudospin symmetries in the Dirac equation with central Coulomb potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multitrace operators and the generalized AdS/CFT prescription

We show that multitrace interactions can be consistently incorporated into an extended AdS conformal field theory (CFT) prescription involving the inclusion of generalized boundary conditions and a modified Legendre transform prescription. We find new and consistent results by considering a self-contained formulation which relates the quantization of the bulk theory to the AdS/CFT correspondence and the perturbation at the boundary by double-trace interactions. We show that there exist particular double-trace perturbations for which irregular modes are allowed to propagate as well as the regular ones. We perform a detailed analysis of many different possible situations, for both minimally and nonminimally coupled cases. In all situations, we make use of a new constraint which is found by requiring consistency. In the particular nonminimally coupled case, the natural extension of the Gibbons-Hawking surface term is generated.

Lessons of spin and torsion: Reply to Consistent coupling to Dirac fields in teleparallelism

In reply to the criticism made by Mielke in the preceding Comment on our recent paper, we once again explicitly demonstrate the inconsistency of the coupling of a Dirac field to gravitation in the teleparallel equivalent of general relativity. Moreover, we stress that the mentioned inconsistency is generic for all sources with spin and is by no means restricted to the Dirac field. In this sense the SL(4,R)-covariant generalization of the spinor fields in the teleparallel gravity theory is irrelevant to the inconsistency problem.

Vertex operators and soliton solutions of affine Toda model with U(2) symmetry

The symmetry structure of the non-Abelian affine Toda model based on the coset SL(3)/SL(2) circle times U(1) is studied. It is shown that the model possess non-Abelian Noether symmetry closing into a q-deformed SL(2) circle times U(1) algebra. Specific two-vertex soliton solutions are constructed.

Pure spinor vertex operators in Siegel gauge and loop amplitude regularization

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

Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Schrodinger and Pauli-Dirac Oscillators in Noncommutative Phase Space

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)