Searcharxiv⌕ Search

arXiv subjects

A. E. Goncalves

Publications and source records attributed to A. E. Goncalves.

17 recordsLinked to original sources
arXiv2019

Elliptic Genera and q-Series Development in Analysis, String Theory, and N=2 Superconformal Field Theory

In this article we examine the Ruelle type spectral functions $\cR(s)$,which define an overall description of the content of the work. We investigate the Gopakumar-Vafa reformulation of the string partition functions, describe the N=2 Landau-Ginzburg model in terms of Ruelle type spectral functions. Furthermore, we discuss the basic properties satisfied by elliptic genera in N=2 theories, construct the functional equations for $\cR(s)$, and analyze the modular transformation laws for the elliptic genus of the Landau-Ginzburg model and study their properties in details.

hep-th↗
arXiv2005

Spectral Functions for Gauge Fields in Rindler-Like Spaces

A class of conformal deformations of Rindler-like spaces is analyzed. We study the spectral properties of the Laplace operators associated with $p-$forms and acting in these spaces and in their spatial sections. The spectral density of continuum spectrum and the spectral zeta functions related to the abelian $p-$forms in real compact hyperbolic manifolds are obtained.

hep-th↗
arXiv2000

One-loop effective potential for scalar and vector fields on higher dimensional noncommutative flat manifolds

The effective potentials for massless scalar and vector quantum field theories on D dimensional manifolds with p compact noncommutative extra dimensions are evaluated by means of dimensional regularization implemented by zeta function techniques. It is found that the zeta function associated with the one-loop operator may not be regular at the origin. Thus, the related heat-kernel trace has a logarithmic term in the short t asymptotics expansion. Consequences of this fact are briefly discussed.

hep-th↗
arXiv2000

QED in external field with space-time uniform invariants. Exact solutions

We study exact solutions of Dirac and Klein-Gordon equations and Green functions in d-dimensional QED and in an external electromagnetic field with constant and homogeneous field invariants. The cases of even and odd dimensions are considered separately, they are essentially different. We direct attention to the asymmetry of the quasienergy spectrum, which appears in odd dimensions. The in and out classification of the exact solutions as well as the completeness and orthogonality relations is strictly proven. Different Green functions in the form of sums over the exact solutions are constructed. The Fock-Schwinger proper time integral representations of these Green functions are found. As physical applications we consider the calculations of different quantum effects related to the vacuum instability in the external field. For example, we present mean values of particles created from the vacuum, the probability of the vacuum remaining a vacuum, the effective action, and the expectation values of the current and energy-momentum tensor.

hep-th↗
arXiv2000

Quantum spinor field in the FRW universe with a constant electromagnetic background

The article is a natural continuation of our paper {\em Quantum scalar field in FRW Universe with constant electromagnetic background}, Int. J. Mod. Phys. {\bf A12}, 4837 (1997). We generalize the latter consideration to the case of massive spinor field, which is placed in FRW Universe of special type with a constant electromagnetic field. To this end special sets of exact solutions of Dirac equation in the background under consideration are constructed and classified. Using these solutions representations for out-in, in-in, and out-out spinor Green functions are explicitly constructed as proper-time integrals over the corresponding contours in complex proper-time plane. The vacuum-to-vacuum transition amplitude and number of created particles are found and vacuum instability is discussed. The mean values of the current and energy-momentum tensor are evaluated, and different approximations for them are presented. The back reaction related to particle creation and to the polarization of the unstable vacuum is estimated in different regimes.

hep-th↗
arXiv1999

Chern-Simons Invariants of Closed Hyperbolic 3-Manifolds

The Chern-Simons invariants of irreducible U(n)- flat connections on compact hyperbolic 3-manifolds of the form Γ\H^3 are derived. The explicit formula for the Chern-Simons functional is given in terms of Selberg type zeta functions related to the twisted eta invariants of Atiyah-Patodi-Singer.

hep-th↗
arXiv1999

Mass and Decay Spectra of the Piecewise Uniform String

Mass and decay spectra are calculated for quantum massive excitations of a piecewise uniform bosonic string. The physical meaning of the critical temperatures characterizing the radiation in the decay of a massive microstate in string theory is discussed.

hep-th↗
arXiv1999

Anomalies and Analytic Torsion on Hyperbolic Manifolds

The global additive and multiplicative properties of the Laplacian on j-forms and related zeta functions are analyzed. The explicit form of zeta functions on a product of closed oriented hyperbolic manifolds Γ\backslash{\Bbb H}^d and of the multiplicative anomaly are derived. We also calculate in an explicit form the analytic torsion associated with a connected sum of such manifolds.

hep-th↗
arXiv1997

The Conformal Anomaly in General Rank 1 Symmetric Spaces and Associated Operator Product

We compute the one-loop effective action and the conformal anomaly associated with the product $\bigotimes_p{\cal L}_p$ of the Laplace type operators ${\cal L}_p, p=1,2$, acting in irreducible rank 1 symmetric spaces of non-compact type. The explicit form of the zeta functions and the conformal anomaly of the stress-energy momentum tensor is derived.

hep-th↗
arXiv1997

Brane-Black Hole Correspondence and Asymptotics of Quantum Spectrum

We discuss the asymptotic properties of quantum states density for fundamental (super) membrane in the semiclassical approach. The matching of BPS part of spectrum for superstring and supermembrane gives the possibility to get stringy results via membrane calculations and vice versa. The brane-black hole correspondence (on the level of black hole states and brane microstates) is also studied.

hep-th↗
arXiv1996

Pseudoclassical description of the massive Dirac particles in odd dimensions

A pseudoclassical model is proposed to describe massive Dirac (spin one-half) particles in arbitrary odd dimensions. The quantization of the model reproduces the minimal quantum theory of spinning particles in such dimensions. A dimensional duality between the model proposed and the pseudoclassical description of Weyl particles in even dimensions is discussed.

hep-th↗
arXiv1994

New Pseudoclassical model for Weyl particles

A new pseudoclassical model to describe Weyl particles is proposed. Different ways of its quantization are presented. They all lead to the theory of Weyl particle; namely, the massless Dirac equation and the Weyl condition are reproduced. In contrast with models discussed previously, this one admits both the Dirac quantization and quasicanonical quantization, with the fixation of almost all gauge freedom on the classical level.

hep-th↗