8,207 research outputs found
Subtleties in the beta function calculation of N=1 supersymmetric gauge theories
We investigate some peculiarities in the calculation of the two-loop
beta-function of supersymmetric models which are intimately related to
the so-called "Anomaly Puzzle". There is an apparent paradox when the
computation is performed in the framework of the covariant derivative
background field method. In this formalism, it is obtained a finite two-loop
effective action, although a non-null coefficient for the beta-function is
achieved by means of the renormalized two-point function in the background
field. We show that if the standard background field method is used, this
two-point function has a divergent part which allows for the calculation of the
beta-function via the renormalization constants, as usual. Therefore, we
conjecture that this paradox has its origin in the covariant supergraph
formalism itself, possibly being an artifact of the rescaling anomaly.Comment: Few misprintings corrected and comments added. To meet the version to
be published at European Physical Journal
Conductivity of Coulomb interacting massless Dirac particles in graphene: Regularization-dependent parameters and symmetry constraints
We compute the Coulomb correction to the a. c. conductivity of
interacting massless Dirac particles in graphene in the collisionless limit
using the polarization tensor approach in a regularization independent
framework. Arbitrary parameters stemming from differences between
logarithmically divergent integrals are fixed on physical grounds exploiting
only spatial rotational invariance of the model which amounts to
transversality of the polarization tensor. Consequently is
unequivocally determined to be within this effective model. We
compare our result with explicit regularizations and discuss the origin of
others results for found in the literature
Ultraviolet and Infrared Divergences in Implicit Regularization: a Consistent Approach
Implicit Regularization is a 4-dimensional regularization initially conceived
to treat ultraviolet divergences. It has been successfully tested in several
instances in the literature, more specifically in those where Dimensional
Regularization does not apply. In the present contribution we extend the method
to handle infrared divergences as well. We show that the essential steps which
rendered Implicit Regularization adequate in the case of ultraviolet
divergences have their counterpart for infrared ones. Moreover we show that a
new scale appears, typically an infrared scale which is completely independent
of the ultraviolet one. Examples are given.Comment: 9 pages, version to appear in Mod. Phys. Lett.
One-loop conformal anomaly in an implicit momentum space regularization framework
In this paper we consider matter fields in a gravitational background in
order to compute the breaking of the conformal current at one-loop order.
Standard perturbative calculations of conformal symmetry breaking expressed by
the non-zero trace of the energy-momentum tensor have shown that some violating
terms are regularization dependent, which may suggest the existence of spurious
breaking terms in the anomaly. Therefore, we perform the calculation in a
momentum space regularization framework in which regularization dependent terms
are judiciously parametrized. We compare our results with those obtained in the
literature and conclude that there is an unavoidable arbitrariness in the
anomalous term .Comment: in European Physical Journal C, 201
The Casimir spectrum revisited
We examine the mathematical and physical significance of the spectral density
sigma(w) introduced by Ford in Phys. Rev. D38, 528 (1988), defining the
contribution of each frequency to the renormalised energy density of a quantum
field. Firstly, by considering a simple example, we argue that sigma(w) is well
defined, in the sense of being regulator independent, despite an apparently
regulator dependent definition. We then suggest that sigma(w) is a spectral
distribution, rather than a function, which only produces physically meaningful
results when integrated over a sufficiently large range of frequencies and with
a high energy smooth enough regulator. Moreover, sigma(w) is seen to be simply
the difference between the bare spectral density and the spectral density of
the reference background. This interpretation yields a simple `rule of thumb'
to writing down a (formal) expression for sigma(w) as shown in an explicit
example. Finally, by considering an example in which the sign of the Casimir
force varies, we show that the spectrum carries no manifest information about
this sign; it can only be inferred by integrating sigma(w).Comment: 10 pages, 4 figure
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