Nonassociative geometry: Towards discrete structure of spacetime

In the framework of nonassociative geometry (hep-th/0003238) a unified description of continuum and discrete spacetime is proposed. In our approach at the Planck scales the spacetime is described as a so-called "diodular discrete structure" which at large spacetime scales `looks like' a differentiable manifold. After a brief review of foundations of nonassociative geometry,we discuss the nonassociative smooth and discrete de Sitter spacetimes.Comment: RevTex file, 5 pages, typos correcte

Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity

A new quasigroup approach to conservation laws in general relativity is applied to study asymptotically flat at future null infinity spacetime. The infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to the Poincar\'e quasigroup and the Noether charge associated with any element of the Poincar\'e quasialgebra is defined. The integral conserved quantities of energy-momentum and angular momentum are linear on generators of Poincar\'e quasigroup, free of the supertranslation ambiguity, posess the flux and identically equal to zero in Minkowski spacetime.Comment: RevTeX4, 5 page

Smooth Loops and Fiber Bundles: Theory of Principal Q-bundles

A nonassociative generalization of the principal fiber bundles with a smooth loop mapping on the fiber is presented. Our approach allows us to construct a new kind of gauge theories that involve higher ''nonassociative'' symmetries.Comment: 20 page

Wolff-Type Embedding Algorithms for General Nonlinear σ\sigma-Models

We study a class of Monte Carlo algorithms for the nonlinear $\sigma$-model, based on a Wolff-type embedding of Ising spins into the target manifold $M$. We argue heuristically that, at least for an asymptotically free model, such an algorithm can have dynamic critical exponent $z \ll 2$ only if the embedding is based on an (involutive) isometry of $M$ whose fixed-point manifold has codimension 1. Such an isometry exists only if the manifold is a discrete quotient of a product of spheres. Numerical simulations of the idealized codimension-2 algorithm for the two-dimensional $O(4)$-symmetric $\sigma$-model yield $z_{int,{\cal M}^2} = 1.5 \pm 0.5$ (subjective 68\% confidence interval), in agreement with our heuristic argument.Comment: 70 pages, 7 postscript figure

Estimation of orbital velocities of internal waves of short period and large amplitudes

Se expone un método para la determinación de la componente horizontal de la velocidad orbital de las ondas internas de gran amplitud desde una embarcación en movimiento. El método se fundamenta en el conocimiento de la respuesta en frecuencia del frenado de la embarcación y del análisis del registro en bitácora de la oscilación de la velocidad en el campo de las ondas internas. Se discuten datos obtenidos en la zona de unos bajos en la parte central del océano lndico