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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
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