Non perturbative regularization of one loop integrals at finite temperature

A method devised by the author is used to calculate analytical expressions for one loop integrals at finite temperature. A non-perturbative regularization of the integrals is performed, yielding expressions of non-polynomial nature. A comparison with previuosly published results is presented and the advantages of the present technique are discussed.Comment: 7 pages, 2 figures, 2 tables; corrected some typos and simplified eq. (8

A perturbative approach to the spectral zeta functions of strings, drums and quantum billiards

We have obtained an explicit expression for the spectral zeta functions and for the heat kernel of strings, drums and quantum billiards working to third order in perturbation theory, using a generalization of the binomial theorem to operators. The perturbative parameter used in the expansion is either the small deformation of a reference domain (for instance a square), or a small variation of the density around a constant value (in two dimensions both cases can apply). This expansion is well defined even in presence of degenerations of the unperturbed spectrum. We have discussed several examples in one, two and three dimensions, obtaining in some cases the analytic continuation of the series, which we have then used to evaluate the corresponding Casimir energy. For the case of a string with piecewise constant density, subject to different boundary conditions, and of two concentric cylinders of very close radii, we have reproduced results previously published, thus obtaining a useful check of our method.Comment: 23 pages, 5 figures, 2 tables; version accepted on Journal of Mathematical Physic

The emergence of AdS(2) from quantum fluctuations

We have shown how the quantization of two-dimensional quantum gravity with an action which contains only a positive cosmological constant and boundary cosmological constants leads to the emergence of a spacetime which can be described as a constant negative curvature spacetime with superimposed quantum fluctuations.Comment: 4 pages. Talk given by W. Westra at the Eleventh Marcel Grossmann Meeting on General Relativity at the Freie U. Berlin, July 23 - 29, 200

Colour superconductivity in finite systems

In this paper we study the effect of finite size on the two-flavour colour superconducting state. As well as restricting the quarks to a box, we project onto states of good baryon number and onto colour singlets, these being necessary restrictions on any observable ``quark nuggets''. We find that whereas finite size alone has a significant effect for very small boxes, with the superconducting state often being destroyed, the effect of projection is to restore it again. The infinite-volume limit is a good approximation even for quite small systems.Comment: 14 pages RevTeX4, 12 eps figure

Aspects of the Color Flavor Locking phase of QCD in the Nambu-Jona Lasinio approximation

We study two aspects of the CFL phase of QCD in the NJL approximation. The first one is the issue of the dependence on \mu of the ultraviolet cutoff in the gap equation, which is solved allowing a running coupling constant. The second one is the dependence of the gap on the strange quark mass; using the high density effective theory we perform an expansion in the parameter (m_s/\mu)^2 after checking that its numerical validity is very good already at first order.Comment: LaTeX file, 6 figure

Relativistic Hamiltonians in many-body theories

We discuss the description of a many-body nuclear system using Hamiltonians that contain the nucleon relativistic kinetic energy and potentials with relativistic corrections. Through the Foldy-Wouthuysen transformation, the field theoretical problem of interacting nucleons and mesons is mapped to an equivalent one in terms of relativistic potentials, which are then expanded at some order in 1/m_N. The formalism is applied to the Hartree problem in nuclear matter, showing how the results of the relativistic mean field theory can be recovered over a wide range of densities.Comment: 14 pages, uses REVTeX and epsfig, 3 postscript figures; a postscript version of the paper is available by anonymous ftp at ftp://carmen.to.infn.it/pub/depace/papers/951

Chiral quark-soliton model in the Wigner-Seitz approximation

In this paper we study the modification of the properties of the nucleon in the nucleus within the quark-soliton model. This is a covariant, dynamical model, which provides a non-linear representation of the spontaneously broken SU(2)_L X SU(2)_R symmetry of QCD. The effects of the nuclear medium are accounted for by using the Wigner-Seitz approximation and therefore reducing the complex many-body problem to a simpler single-particle problem. We find a minimum in the binding energy at finite density, a change in the isoscalar nucleon radius and a reduction of the in-medium pion decay constant. The latter is consistent with a partial restoration of chiral symmetry at finite density, which is predicted by other models.Comment: 30 pages, 13 figures; uses REVTeX and epsfi

Color-Neutral Superconducting Quark Matter

We investigate the consequences of enforcing local color neutrality on the color superconducting phases of quark matter by utilizing the Nambu-Jona-Lasinio model supplemented by diquark and the t'Hooft six-fermion interactions. In neutrino free matter at zero temperature, color neutrality guarantees that the number densities of u, d, and s quarks in the Color-Flavor-Locked (CFL) phase will be equal even with physical current quark masses. Electric charge neutrality follows as a consequence and without the presence of electrons. In contrast, electric charge neutrality in the less symmetric 2-flavor superconducting (2SC) phase with ud pairing requires more electrons than the normal quark phase. The free energy density cost of enforcing color and electric charge neutrality in the CFL phase is lower than that in the 2SC phase, which favors the formation of the CFL phase. With increasing temperature and neutrino content, an unlocking transition occurs from the CFL phase to the 2SC phase with the order of the transition depending on the temperature, the quark and lepton number chemical potentials. The astrophysical implications of this rich structure in the phase diagram, including estimates of the effects from Goldstone bosons in the CFL phase, are discussed.Comment: 20 pages, 4 figures; version to appear in Phys. Rev.

Chiral phase properties of finite size quark droplets in the Nambu--Jona-Lasinio model

Chiral phase properties of finite size hadronic systems are investigated within the Nambu--Jona-Lasinio model. Finite size effects are taken into account by making use of the multiple reflection expansion. We find that, for droplets with relatively small baryon numbers, chiral symmetry restoration is enhanced by the finite size effects. However the radius of the stable droplet does not change much, as compared to that without the multiple reflection expansion.Comment: RevTex4, 9 pages, 6 figures, to be published in Phys. Rev.

Gravitational Lensing by Black Holes

We review the theoretical aspects of gravitational lensing by black holes, and discuss the perspectives for realistic observations. We will first treat lensing by spherically symmetric black holes, in which the formation of infinite sequences of higher order images emerges in the clearest way. We will then consider the effects of the spin of the black hole, with the formation of giant higher order caustics and multiple images. Finally, we will consider the perspectives for observations of black hole lensing, from the detection of secondary images of stellar sources and spots on the accretion disk to the interpretation of iron K-lines and direct imaging of the shadow of the black hole.Comment: Invited article for the GRG special issue on lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). 31 pages, 12 figure