On the Classification of Automorphic Lie Algebras

It is shown that the problem of reduction can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of these algebras, beyond the context of integrable systems. Moreover, it is proven that sl2-Automorphic Lie Algebras associated to the icosahedral group I, the octahedral group O, the tetrahedral group T, and the dihedral group Dn are isomorphic. The proof is based on techniques from classical invariant theory and makes use of Clebsch-Gordan decomposition and transvectants, Molien functions and the trace-form. This result provides a complete classification of sl2-Automorphic Lie Algebras associated to finite groups when the group representations are chosen to be the same and it is a crucial step towards the complete classification of Automorphic Lie Algebras.Comment: 29 pages, 1 diagram, 9 tables, standard LaTeX2e, submitted for publicatio

Reduction Groups and Automorphic Lie Algebras

We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates the name automorphic Lie algebras. For automorphic Lie algebras we present bases in which they are quasigraded and all structure constants can be written out explicitly. These algebras have a useful factorisations on two subalgebras similar to the factorisation of the current algebra on the positive and negative parts.Comment: 21 pages, standard LaTeX2e, corrected typos, accepted for publication in CMP - Communications in Mathematical Physic

Medium polarization in asymmetric nuclear matter

The influence of the core polarization on the effective nuclear interaction of asymmetric nuclear matter is calculated in the framework of the induced interaction theory. The strong isospin dependence of the density and spin density fluctuations is studied along with the interplay between the neutron and proton core polarizations. Moving from symmetric nuclear matter to pure neutron matter the crossover of the induced interaction from attractive to repulsive in the spin singlet state is determined as a function of the isospin imbalance.The density range in which it occurs is also determined. For the spin triplet state the induced interaction turns out to be always repulsive. The implications of the results for the neutron star superfluid phases are shortly discussed.Comment: 6 pages, 4 figure

Model study of the sign problem in the mean-field approximation

We argue the sign problem of the fermion determinant at finite density. It is unavoidable not only in Monte-Carlo simulations on the lattice but in the mean-field approximation as well. A simple model deriving from Quantum Chromodynamics (QCD) in the double limit of large quark mass and large quark chemical potential exemplifies how the sign problem arises in the Polyakov loop dynamics at finite temperature and density. In the color SU(2) case our mean-field estimate is in excellent agreement with the lattice simulation. We combine the mean-field approximation with a simple phase reweighting technique to circumvent the complex action encountered in the color SU(3) case. We also investigate the mean-field free energy, from the saddle-point of which we can estimate the expectation value of the Polyakov loop.Comment: 14 page, 18 figures, typos corrected, references added, some clarification in sec.I

Neural endophenotypes of social behaviour in autism spectrum conditions

Autism is characterized by qualitative impairments in social interaction, communication, and stereotyped repetitive behaviors and/or restricted interests. Beyond these diagnostic criteria, autism is viewed as a neurodevelopmental condition with possibly several etiologies that manifest in complex patterns of atypical structural and functional brain development, cognition, and behavior. Despite the multidimensional nature of and substantial variation within the autism spectrum, impairments in social interaction remain among the most visible hallmarks of the condition. It is this profound developmental deficit in the social domain that makes autism a unique case in the field of social neuroscience. This chapter contributes to the dialogue amongst both the fields of autism research and social neuroscience by deliberately taking the stance of asking how we can understand more about the etiological mechanisms underlying social behavior in autism. It presents a multi-level overview of the literature on the behavioral, neural, and genetic underpinnings of social functioning in autism spectrum conditions (ASC). The main objective is to highlight the current state of the field regarding theory of mind/empathy difficulties in ASC, and then to suggest distinct candidate neural endophenotypes that can bridge the gap between social behavior and genetic mechanisms

SU(2) Glueballs, diquarks and mesons in dense matter

We present preliminary results from a high statistics study of 2-color QCD at low temperature and non-zero baryon density. The simulations are carried out on a 6^3*12 lattice and use a standard hybrid molecular dynamics algorithm for staggered fermions for two values of quark mass. Observables include glueball correlators evaluated via a multi-step smearing procedure as well as scalar and vector mesons and diquarks.Comment: Poster presented at Lattice 2003 (Non zero temperature and density), 3 pages, 4 figure

New spherically symmetric monopole and regular solutions in Einstein-Born-Infeld theories

In this work a new asymptotically flat solution of the coupled Einstein-Born-Infeld equations for a static spherically symmetric space-time is obtained. When the intrinsic mass is zero the resulting spacetime is regular everywhere, in the sense given by B. Hoffmann and L. Infeld in 1937, and the Einstein-Born-Infeld theory leads to the identification of the gravitational with the electromagnetic mass. This means that the metric, the electromagnetic field and their derivatives have not discontinuities in all the manifold. In particular, there are not conical singularities at the origin, in contrast to well known monopole solution studied by B. Hoffmann in 1935. The lack of uniqueness of the action function in Non-Linear-Electrodynamics is discussed.Comment: Final version in journal. Amplied version with new results that previous talk in Protvino worksho

Glueballs and mesons in the superfluid phase of two-color QCD

QCD with two colors undergoes a transition to a superfluid phase with diquark condensate when the quark chemical potential equals half the pion mass. We investigate the gluonic aspects of the transition by inspecting the behavior of the glueball correlators evaluated via a multi-step smearing procedure for several values of chemical potential ranging between zero and the saturation threshold. The results are based on an analysis of 0++ glueball correlators, on a sample of 40000 independent configurations on each parameter set. The amplitudes of the correlators peak for \mu = m_\pi/2,indicating that the superfluid phase transition affects the gluonic sector as well. The mass of the fundamental state decreases in the superfluid phase, and the amplitude of the propagators drops, suggesting a reduction of the gluon condensate, in agreement with model calculations. The analysis of the smearing dependence of the results helps disentangling the role of long and short distance phenomena at the superfluid transition.Comment: 7 pages, 5 figures, talk presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4, 2007, Regensburg,German