Momentum Space Regularizations and the Indeterminacy in the Schwinger Model

We revisited the problem of the presence of finite indeterminacies that appear in the calculations of a Quantum Field Theory. We investigate the occurrence of undetermined mathematical quantities in the evaluation of the Schwinger model in several regularization scenarios. We show that the undetermined character of the divergent part of the vacuum polarization tensor of the model, introduced as an {\it ansatz} in previous works, can be obtained mathematically if one introduces a set of two parameters in the evaluation of these quantities. The formal mathematical properties of this tensor and their violations are discussed. The analysis is carried out in both analytical and sharp cutoff regularization procedures. We also show how the Pauli Villars regularization scheme eliminates the indeterminacy, giving a gauge invariant result in the vector Schwinger model.Comment: 10 pages, no figure

A generalization of the S-function method applied to a Duffing-Van der Pol forced oscillator

In [1,2] we have developed a method (we call it the S-function method) that is successful in treating certain classes of rational second order ordinary differential equations (rational 2ODEs) that are particularly `resistant' to canonical Lie methods and to Darbouxian approaches. In this present paper, we generalize the S-function method making it capable of dealing with a class of elementary 2ODEs presenting elementary functions. Then, we apply this method to a Duffing-Van der Pol forced oscillator, obtaining an entire class of first integrals

Diamagnetic response of cylindrical normal metal - superconductor proximity structures with low concentration of scattering centers

We have investigated the diamagnetic response of composite NS proximity wires, consisting of a clean silver or copper coating, in good electrical contact to a superconducting niobium or tantalum core. The samples show strong induced diamagnetism in the normal layer, resulting in a nearly complete Meissner screening at low temperatures. The temperature dependence of the linear diamagnetic susceptibility data is successfully described by the quasiclassical Eilenberger theory including elastic scattering characterised by a mean free path l. Using the mean free path as the only fit parameter we found values of l in the range 0.1-1 of the normal metal layer thickness d_N, which are in rough agreement with the ones obtained from residual resistivity measurements. The fits are satisfactory over the whole temperature range between 5 mK and 7 K for values of d_N varying between 1.6 my m and 30 my m. Although a finite mean free path is necessary to correctly describe the temperature dependence of the linear response diamagnetic susceptibility, the measured breakdown fields in the nonlinear regime follow the temperature and thickness dependence given by the clean limit theory. However, there is a discrepancy in the absolute values. We argue that in order to reach quantitative agreement one needs to take into account the mean free path from the fits of the linear response. [PACS numbers: 74.50.+r, 74.80.-g]Comment: 10 pages, 9 figure

Solving 1ODEs with functions

Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background to deal, in the extended Prelle-Singer approach context, with systems of 1ODEs. In this present paper, we will apply these results in order to produce a method that is more efficient in a great number of cases. Directly, the solving of 1ODEs is applicable to any problem presenting parameters to which the rate of change is related to the parameter itself. Apart from that, the solving of 1ODEs can be a part of larger mathematical processes vital to dealing with many problems.Comment: 31 page

The cosmological behavior of Bekenstein's modified theory of gravity

We study the background cosmology governed by the Tensor-Vector-Scalar theory of gravity proposed by Bekenstein. We consider a broad family of potentials that lead to modified gravity and calculate the evolution of the field variables both numerically and analytically. We find a range of possible behaviors, from scaling to the late time domination of either the additional gravitational degrees of freedom or the background fluid.Comment: 10 pages, 8 figures, A few typos corrected in the text and figures. Version published in PR