On the entropy operator for the general SU(1,1) TFD formulation

In this Letter, an entropy operator for the general unitary SU(1, 1) TFD formulation is proposed and used to lead a bosonic system from zero to finite temperature. Namely, considering the closed bosonic string as the target system, the entropy operator is used to construct the thermal vacuum. The behaviour of such a state under the breve conjugation rules is analyzed and it was shown that the breve conjugation does not affect the thermal effects. From this thermal vacuum the thermal energy, the entropy and the free energy of the closed bosonic string are calculated and the appropriated thermal distribution for the system is found after the free energy minimization. (C) 2004 Elsevier B.V. All rights reserved.

Massive superstring vertex operator in D=10 superspace

Using the pure spinor formalism for the superstring, the vertex operator for the first massive states of the open superstring is constructed in a manifestly super-Poincare covariant manner. This vertex operator describes a massive spin-two multiplet in terms of ten-dimensional superfields.

Entanglement and entropy operator for strings in pp-wave time dependent background

In this Letter new aspects of string theory propagating in a pp-wave time dependent background with a null singularity are explored. It is shown the appearance of a 2d entanglement entropy dynamically generated by the background. For asymptotically flat observers, the vacuum close to the singularity is unitarily inequivalent to the vacuum at tau = -infinity and it is shown that the 2d entanglement entropy diverges close to this point. As a consequence. The positive time region is inaccessible for observers in tau = -infinity. For a stationary measure, the vacuum at finite time is seen by those observers as a thermal state and the information loss is encoded as a heat bath of string states. (c) 2006 Elsevier B.V. All rights reserved.

Tunneling time through a barrier using the local value of a time operator

A time for a quantum particle to traverse a barrier is obtained for stationary states by setting the local value of a time operator equal to a constant. This time operator, called the tempus operator because it is distinct from the time of evolution, is defined as the operator canonically conjugate to the energy operator. The local value of the tempus operator gives a complex time for a particle to traverse a barrier. The method is applied to a particle with a semiclassical wave function, which gives, in the classical limit, the correct classical traversal time. It is also applied to a quantum particle tunneling through a rectangular barrier. The resulting complex tunneling time is compared with complex tunneling times from other methods.

A singular conformal spacetime

The infinite cosmological constant limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which constitutes a new example of maximally-symmetric spacetime. Grounded on its geometric and thermodynamic properties, some speculations are made in connection with the primordial universe. (c) 2005 Elsevier B.V. All rights reserved.

On the N=2 superstring BRST operator

We show that the BRST charge for the N = 2 superstring system can be written as Q = e(-R)(phi dz/2 pi ib gamma(+)gamma(-))e(R), when b and gamma(+/-) are super-reparametrizations ghosts. This provides a trivial proof of the nilpotence of this operator. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Operator ordering in quantum radiative processes

In this work we reexamine quantum electrodynamics of atomic electrons in the Coulomb gauge in the dipole approximation and calculate the shift of atomic energy levels in the context of Dalibard, Dupont-Roc and Cohen-Tannoudji formalism by considering the variation rates of physical observable. We then analyze the physical interpretation of the ordering of operators in the dipole approximation interaction Hamiltonian in terms of field fluctuations and self-reaction of atomic electrons, discussing the arbitrariness in the statistical functions in second-order bound-state perturbation theory. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Generalization of the Hamilton-Jacobi approach for higher-order singular systems

We generalize the Hamilton-Jacobi formulation for higher-order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraints structure present in such systems.

Hamilton-Jacobi approach to Berezinian singular systems

In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed For singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the Hamilton-Jacobi equation for such systems, analyzing the singular case in order to obtain the equations of motion as total differential equations and study the integrability conditions for such equations. An example is solved using both Hamilton-Jacobi and Dirac's Hamiltonian formalisms and the results are compared. (C) 1998 Academic Press.

An effective singular oscillator for Duffin-Kemmer-Petiau particles with a nonminimal vector coupling: a two-fold degeneracy

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Renormalization of singular potentials and power counting

We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r(2) potential perturbed by a 1/r(4) correction. The power-counting rule, an important ingredient of effective theory, is established by seeking the minimum set of short-range counterterms that renormalize the scattering amplitude. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis. (C) 2008 Elsevier B.V. All rights reserved.

A singular approach to discontinuous vector fields on the plane

In this paper we deal with discontinuous vector fields on R-2 and we prove that the analysis of their local behavior around a typical singularity can be treated via singular perturbation. The regularization process developed by Sotomayor and Teixeira is crucial for the development of this work. (c) 2006 Elsevier B.V. All rights reserved.

Regularization of discontinuous vector fields on R-3 via singular perturbation

Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in this paper. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular problem for which the discontinuous set is a center manifold. Moreover, the definition of' sliding vector field coincides with the reduced problem of the corresponding singular problem for a class of vector fields.

PHENOMENOLOGICAL APPLICATION OF THE PROJECTION-OPERATOR METHOD AND ITS CONNECTION WITH CRITICAL-DYNAMICS

We consider the dynamics of a system of interacting spins described by the Ginzburg-Landau Hamiltonian. The method used is Zwanzig's version of the projection-operator method, in contrast to previous derivations in which we used Mori's version of this method. It is proved that both methods produce the same answer for the Green's function. We also make contact between the projection-operator method and critical dynamics.

PATH INTEGRAL AND OPERATOR APPROACH FOR THE PODOLSKY-SCHWINGER MODEL

We study the role of the thachyonic excitation which emerges from the quantum electrodynamics in two dimensions with Podolsky term. The quantization is performed by using path integral framework and the operator approach.