On a refinement of Craig's lattices

Let p be an odd prime. A family of (p - 1)-dimensional over-lattices yielding new record packings for several values of p in the interval [149... 3001] is presented. The result is obtained by modifying Craig's construction and considering conveniently chosen Z-submodules of Q(zeta), where zeta is a primitive pth root of unity. For p >= 59, it is shown that the center density of the (p - 1)-dimensional lattice in the new family is at least twice the center density of the (p - 1)-dimensional Craig lattice. (C) 2010 Elsevier B.V. All rights reserved.

ON THE MINIMUM ABSOLUTE VALUE of THE DISCRIMINANT of ABELIAN FIELDS of DEGREE p(2)

Let p be a prime number. A formula for the minimum absolute value of the discriminant of all Abelian extensions of Q of degree p(2) is given in terms of p.

Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure

We discuss the q-state Potts models for q less than or equal to 4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions of all critical points, and for the tricritical points when 4 > q greater than or equal to 2. We also note a curious appearance of the extended last line of Freudenthal's magic square in connection with the Potts models. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Mapping the Wigner distribution function of the Morse oscillator onto a semiclassical distribution function

The mapping of the Wigner distribution function (WDF) for a given bound state onto a semiclassical distribution function (SDF) satisfying the Liouville equation introduced previously by us is applied to the ground state of the Morse oscillator. The purpose of the present work is to obtain values of the potential parameters represented by the number of levels in the case of the Morse oscillator, for which the SDF becomes a faithful approximation of the corresponding WDF. We find that for a Morse oscillator with one level only, the agreement between the WDF and the mapped SDF is very poor but for a Morse oscillator of ten levels it becomes satisfactory. We also discuss the limit h --> 0 for fixed potential parameters.

Solitons with isospin

We study the symmetries of the soliton spectrum of a pair of T-dual integrable models, invariant under global SL(2)(q) circle times U(1) transformations. They represent an integrable perturbation of the reduced Gepner parafermions, based on certain gauged SL(3)-WZW model. Their (semiclassical) topological soliton solutions, carrying isospin and belonging to the root of unity representations of q-deformed SU(2)(q)-algebra are obtained. We derive the semiclassical particle spectrum of these models, which is further used to prove their T-duality properties. (c) 2005 Elsevier B.V All rights reserved.

Deformations of N=2 superconformal algebra and supersymmetric two-component Camassa-Holm equation

This paper is concerned with a link between central extensions of N = 2 superconformal algebra and a supersymmetric two-component generalization of the Camassa-Holm equation. Deformations of superconformal algebra give rise to two compatible bracket structures. One of the bracket structures is derived from the central extension and admits a momentum operator which agrees with the Sobolev norm of a co-adjoint orbit element. The momentum operator induces, via Lenard relations, a chain of conserved Hamiltonians of the resulting supersymmetric Camassa-Holm hierarchy.

Integrable aspects of the scaling q-state Potts models II: finite-size effects

We continue our discussion of the q-state Potts models for q less than or equal to 4, in the scaling regimes close to their critical and tricritical points. In a previous paper, the spectrum and full S-matrix of the models on an infinite line were elucidated; here, we consider finite-size behaviour. TBA equations are proposed for all cases related to phi(21) and phi(12) perturbations of unitary minimal models. These are subjected to a variety of checks in the ultraviolet and infrared limits, and compared with results from a recently-proposed non-linear integral equation. A non-linear integral equation is also used to study the flows from tricritical to critical models, over the full range of q. Our results should also be of relevance to the study of the off-critical dilute A models in regimes 1 and 2. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Mass generation from Lie algebra extensions

Applied to the electroweak interactions, the theory of Lie algebra extensions suggests a mechanism by which the boson masses are generated without resource to spontaneous symmetry breaking. It starts from a gauge theory without any additional scalar field. All the couplings predicted by the Weinberg-Salam theory are present, and a few others which are nevertheless consistent within the model.

Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems

We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which the nonlinear Lorentz dilatation effects here pointed out may be detectable, are suggested.

On high Q(2) behavior of the pion form factor for transitions gamma*gamma -> pi(0) and gamma*gamma* -> pi(0) within the nonlocal quark-pion model

The behavior of the transition pion form factor for processes gamma (*)gamma --> pi(0) and gamma (*)gamma (*) --> pi(0) at large values of space-like photon momenta is estimated within the nonlocal covariant quark-pion model. It is shown that, in general, the coefficient of the leading asymptotic term depends dynamically on the ratio of the constituent quark mass and the average virtuality of quarks in the vacuum and kinematically on the ratio of photon virtualities. The kinematic dependence of the transition form factor allows us to obtain the relation between the pion light-cone distribution amplitude and the quark-pion vertex function. The dynamic dependence indicates that the transition form factor gamma (*)gamma -->, pi(0) at high momentum transfers is very sensitive to the nonlocality size of nonperturbative fluctuations in the QCD vacuum. (C) 2000 Elsevier B.V. B.V. All rights reserved.

The generator coordinate method for a reaction coordinate coupled to a harmonic oscillator bath

This paper investigates the usefulness of the generator coordinate method (GCM) for treating the dynamics of a reaction coordinate coupled to a bath of harmonic degrees of freedom. Models for the unimolecular dissociation and isomerization process (proton transfer) are analyzed. The GCM results, presented in analytical form, provide a very good description and are compared to other methods Like the basis set method and multiconfiguration time dependent self-consistent field. (C) 1998 American Institute of Physics. [S0021-9606(98)50934-8].

Vertex operators and soliton solutions of affine Toda model with U(2) symmetry

The symmetry structure of the non-Abelian affine Toda model based on the coset SL(3)/SL(2) circle times U(1) is studied. It is shown that the model possess non-Abelian Noether symmetry closing into a q-deformed SL(2) circle times U(1) algebra. Specific two-vertex soliton solutions are constructed.

Qcd Sum Rules for the G(KK*pi)(Q(2)) form factor

The QCD Sum Rules have been used to evaluate the form factor in the vertex KK*pi. The method of QCD Sum Rules is based on the duality principle in which it is assumed that the hadrons can simultaneously be described in two levels: quarks and hadrons. This work showed that the, axial current, used to describe the meson K is not appropriated to study the form factor.

Sum rules in the oscillator radiation processes

We consider the problem of a harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the oscillator. Instead of doing direct quantum mechanical calculations we establish some sum rules from which we infer the probabilities associated to the different decay processes of the oscillator. Thus, the sum rules allows to show that the transition probabilities between excited levels follow a binomial distribution. (c) 2005 Published by Elsevier B.V.

Nonabelian Toda theories from parafermionic reductions of the WZW model

We investigate a class of conformal nonabelian-Toda models representing noncompact SL(2, R)/U(1) parafermions (PF) interacting with specific abelian Toda theories and having a global U(1) symmetry. A systematic derivation of the conserved currents, their algebras, and the exact solution of these models are presented. An important property of this class of models is the affine SL(2, R)(q) algebra spanned by charges of the chiral and antichiral nonlocal currents and the U(1) charge. The classical (Poisson brackets) algebras of symmetries VG(n), of these models appear to be of mixed PF-WG(n) type. They contain together with the local quadratic terms specific for the W-n-algebras the nonlocal terms similar to the ones of the classical PF-algebra. The renormalization of the spins of the nonlocal currents is the main new feature of the quantum VA(n)-algebras. The quantum VA(2)-algebra and its degenerate representations are studied in detail. (C) 1999 Academic Press.