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

Further analysis of the connected moments expansion

We apply the connected moments expansion to simple quantum--mechanical examples and show that under some conditions the main equations of the approach are no longer valid. In particular we consider two--level systems, the harmonic oscillator and the pure quartic oscillator.Comment: 19 pages; 2 tables; 4 figure

Materials and techniques for spacecraft static charge control

An overview of the design, development, fabrication, and testing of transparent conductive coatings and conductive lattices deposited or formed on high resistivity spacecraft dielectric materials to obtain control static charge buildup on spacecraft external surfaces is presented. Fabrication techniques for the deposition of indium/tin oxide coatings and copper grid networks on Kapton and FEP Teflon films and special frit coatings for OSR and solar cell cover glasses are discussed. The techniques include sputtering, photoetching, silkscreening, and mechanical processes. A facility designed and built to simulate the electron plasma at geosynchronous altitudes is described along with test procedures. The results of material characterizations as well as electron irradiation aging effects in this facility for spacecraft polymers treated to control static charge are presented. The data presents results for electron beam energies up to 30 kV and electron current densities of 30 nA/cm squared. Parameters measured include secondary emission, surface leakage, and through the sample currents as a function of primary beam energy and voltage

Inversion of perturbation series

We investigate the inversion of perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illustrative examples show that in some cases series reversion may improve the accuracy of the results

Influence of nucleonic motion in Relativistic Fermi Gas inclusive responses

Impulsive hadronic descriptions of electroweak processes in nuclei involve two distinctly different elements: one stems from the nuclear many-body physics --- the medium --- which is rather similar for the various inclusive response functions, and the other embodies the responses of the hadrons themselves to the electroweak probe and varies with the channel selected. In this letter we investigate within the context of the relativistic Fermi gas in both the quasi-elastic and $N\to\Delta$ regimes the interplay between these two elements. Specifically, we focus on expansions in the one small parameter in the problem, namely, the momentum of a nucleon in the initial wave function compared with the hadronic scale, the nucleon mass. Both parity-conserving and -violating inclusive responses are studied and the interplay between longitudinal ($L$) and transverse ($T$ and $T'$) contributions is highlighted.Comment: 11 pages, 1 figur

The confined hydrogen atom with a moving nucleus

We study the hydrogen atom confined to a spherical box with impenetrable walls but, unlike earlier pedagogical articles on the subject, we assume that the nucleus also moves. We obtain the ground-state energy approximately by means of first--order perturbation theory and by a more accurate variational approach. We show that it is greater than the one for the case in which the nucleus is clamped at the center of the box. Present approach resembles the well-known treatment of the helium atom with clamped nucleus

A new representation for non--local operators and path integrals

We derive an alternative representation for the relativistic non--local kinetic energy operator and we apply it to solve the relativistic Salpeter equation using the variational sinc collocation method. Our representation is analytical and does not depend on an expansion in terms of local operators. We have used the relativistic harmonic oscillator problem to test our formula and we have found that arbitrarily precise results are obtained, simply increasing the number of grid points. More difficult problems have also been considered, observing in all cases the convergence of the numerical results. Using these results we have also derived a new representation for the quantum mechanical Green's function and for the corresponding path integral. We have tested this representation for a free particle in a box, recovering the exact result after taking the proper limits, and we have also found that the application of the Feynman--Kac formula to our Green's function yields the correct ground state energy. Our path integral representation allows to treat hamiltonians containing non--local operators and it could provide to the community a new tool to deal with such class of problems.Comment: 9 pages ; 1 figure ; refs added ; title modifie

Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results

We develop powerful numerical and analytical techniques for the solution of the Helmholtz equation on general domains. We prove two theorems: the first theorem provides an exact formula for the ground state of an arbirtrary membrane, while the second theorem generalizes this result to any excited state of the membrane. We also develop a systematic perturbative scheme which can be used to study the small deformations of a membrane of circular or square shapes. We discuss several applications, obtaining numerical and analytical results.Comment: 29 pages, 12 figures, 7 tabl

Reply to "Comment on 'Quantization of FRW spacetimes in the presence of a cosmological constant and radiation'"

The Comment by Amore {\it et al.} [gr-qc/0611029] contains a valid criticism of the numerical precision of the results reported in a recent paper of ours [Phys. Rev. D {\bf 73}, 044022 (2006)], as well as fresh ideas on how to characterize a quantum cosmological singularity. However, we argue that, contrary to what is suggested in the Comment, the quantum cosmological models we studied show hardly any sign of singular behavior.Comment: 4 pages, accepted by Physical Review