Peeping into the SU(2) Gauge Vacuum

We study thermalised configurations of SU(2) gauge fields by cooling. An analysis of the effect of cooling is presented and global and statistical information is extracted.Comment: 3 pages, uuencoded compressed postscript file, contribution to LAT 9

Large NN reduction with the Twisted Eguchi-Kawai model

We examine the breaking of $Z_N$ symmetry recently reported for the Twisted Eguchi-Kawai model (TEK). We analyse the origin of this behaviour and propose simple modifications of twist and lattice action that could avoid the problem. Our results show no sign of symmetry breaking and allow us to obtain values of the large $N$ infinite volume string tension in agreement with extrapolations from results based upon straightforward methods.Comment: latex file 14 pages, 4 figure

Structure and evolution of strange attractors in non-elastic triangular billiards

We study pinball billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls are non-elastic: the outgoing angle with the normal vector to the boundary is a uniform factor $\lambda < 1$ smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter $\lambda$ is varied. For $\lambda$ in the interval (0, 1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of $\lambda$ the billiard dynamics gives rise to nonaccessible regions in phase space. For $\lambda$ close to 1, the attractor splits into three transitive components, the basins of attraction of which have fractal basin boundaries.Comment: 12 pages, 10 figures; submitted for publication. One video file available at http://sistemas.fciencias.unam.mx/~dsanders

Real-time Quantum evolution in the Classical approximation and beyond

With the goal in mind of deriving a method to compute quantum corrections for the real-time evolution in quantum field theory, we analyze the problem from the perspective of the Wigner function. We argue that this provides the most natural way to justify and extend the classical approximation. A simple proposal is presented that can allow to give systematic quantum corrections to the evolution of expectation values and/or an estimate of the errors committed when using the classical approximation. The method is applied to the case of a few degrees of freedom and compared with other methods and with the exact quantum results. An analysis of the dependence of the numerical effort involved as a function of the number of variables is given, which allow us to be optimistic about its applicability in a quantum field theoretical context.Comment: 32 pages, 6 figure

Calorons on the lattice - a new perspective

We discuss the manifestation of instanton and monopole solutions on a periodic lattice at finite temperature and their relation to the infinite volume analytic caloron solutions with asymptotic non-trivial Polyakov loops. As a tool we use improved cooling and twisted boundary conditions. Typically we find 2Q lumps for topological charge Q. These lumps are BPS monopoles.Comment: Latex. 16 pages, 9 figure

Recent results on self-dual configurations on the torus

We review the recent progress on our understanding of self-dual SU(N) Yang-Mills configurations on the torus.Comment: Latex 3 pages, 1 figure. Contribution to the Lat99 Proceeding

Relaciones privadas internacionales en el MERCOSUR y en la Unión Europea

Ponencia recogida en las actas de los Cursos de Derecho Internacional y Relaciones Internacionales de Vitoria-Gasteiz organizados por la Facultad de Derecho de la Universidad del País VascoSe analizan en los dos sistemas de integración: MERCOSUR y Unión Europea, las estructuras institucionales y normativas (dimensión jurídica general de la integración), los modelos de mercado integrado (dimensión económico-comercial) y los aspectos propios de las relaciones típicas de Derecho internacional privado afectadas (dimensión jurídica particular de las relaciones privadas internacionales). También las libertades de circulación en el espacio integrado y los contratos internacionales como cauce jurídico de las relaciones de contenido patrimonialAre analyzed the institutional and regulatory structures (general legal dimension of integration), the integrated market models (economic-commercial dimension) and aspects of the typical international law relation affected private sector (private legal dimension of private international relations) in two integration systems MERCOSUR and European Union. Also the freedoms of movement in the integrated space and international contracts as a legal channel of relations of heritage conten