22,062 research outputs found
Constructive algebraic renormalization of the abelian Higgs-Kibble model
We propose an algorithm, based on Algebraic Renormalization, that allows the
restoration of Slavnov-Taylor invariance at every order of perturbation
expansion for an anomaly-free BRS invariant gauge theory. The counterterms are
explicitly constructed in terms of a set of one-particle-irreducible Feynman
amplitudes evaluated at zero momentum (and derivatives of them). The approach
is here discussed in the case of the abelian Higgs-Kibble model, where the zero
momentum limit can be safely performed. The normalization conditions are
imposed by means of the Slavnov-Taylor invariants and are chosen in order to
simplify the calculation of the counterterms. In particular within this model
all counterterms involving BRS external sources (anti-fields) can be put to
zero with the exception of the fermion sector.Comment: Jul, 1998, 31 page
Reconstructing Rational Functions with
We present the open-source library for the
reconstruction of multivariate rational functions over finite fields. We
discuss the involved algorithms and their implementation. As an application, we
use in the context of integration-by-parts reductions and
compare runtime and memory consumption to a fully algebraic approach with the
program .Comment: 46 pages, 3 figures, 6 tables; v2: matches published versio
S-pairing in neutron matter. I. Correlated Basis Function Theory
S-wave pairing in neutron matter is studied within an extension of correlated
basis function (CBF) theory to include the strong, short range spatial
correlations due to realistic nuclear forces and the pairing correlations of
the Bardeen, Cooper and Schrieffer (BCS) approach. The correlation operator
contains central as well as tensor components. The correlated BCS scheme of
Ref. [Nucl. Phys. A363 (1981) 383], developed for simple scalar correlations,
is generalized to this more realistic case. The energy of the correlated pair
condensed phase of neutron matter is evaluated at the two--body order of the
cluster expansion, but considering the one--body density and the corresponding
energy vertex corrections at the first order of the Power Series expansion.
Based on these approximations, we have derived a system of Euler equations for
the correlation factors and for the BCS amplitudes, resulting in correlated non
linear gap equations, formally close to the standard BCS ones. These equations
have been solved for the momentum independent part of several realistic
potentials (Reid, Argonne v_{14} and Argonne v_{8'}) to stress the role of the
tensor correlations and of the many--body effects. Simple Jastrow correlations
and/or the lack of the density corrections enhance the gap with respect to
uncorrelated BCS, whereas it is reduced according to the strength of the tensor
interaction and following the inclusion of many--body contributions.Comment: 20 pages, 8 figures, 1 tabl
Stochastic area distributions: optimal trajectories, Maslov indices and asymptotic results
In this paper we study the semi-classical approximation for the distribution of area associated with (i) planar polymer rings constrained to enclose a fixed algebraic area and (ii) planar rings subject to an external electric field and constrained to enclose a fixed algebraic area. We demonstrate that the results are accurate in the asymptotic regime. Moreover, we also show that in case (i) it is possible to reconstruct the exact expression for the distribution, provided the contributions from all optimal trajectories are taken into account, as well as the proper Maslov indices
Instantaneous Bethe-Salpeter equation: utmost analytic approach
The Bethe-Salpeter formalism in the instantaneous approximation for the
interaction kernel entering into the Bethe-Salpeter equation represents a
reasonable framework for the description of bound states within relativistic
quantum field theory. In contrast to its further simplifications (like, for
instance, the so-called reduced Salpeter equation), it allows also the
consideration of bound states composed of "light" constituents. Every
eigenvalue equation with solutions in some linear space may be (approximately)
solved by conversion into an equivalent matrix eigenvalue problem. We
demonstrate that the matrices arising in these representations of the
instantaneous Bethe-Salpeter equation may be found, at least for a wide class
of interactions, in an entirely algebraic manner. The advantages of having the
involved matrices explicitly, i.e., not "contaminated" by errors induced by
numerical computations, at one's disposal are obvious: problems like, for
instance, questions of the stability of eigenvalues may be analyzed more
rigorously; furthermore, for small matrix sizes the eigenvalues may even be
calculated analytically.Comment: LaTeX, 23 pages, 2 figures, version to appear in Phys. Rev.
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