Smooth Loops, Generalized Coherent States and Geometric Phases

A description of generalized coherent states and geometric phases in the light of the general theory of smooth loops is given.Comment: LATeX file, 11 page

The principle of relative locality

We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of momentum space with a metric compatible connection and constant curvature.Comment: 12 pages, 3 figures; in version 2 one reference added and some minor modifications in sects. II and III mad

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

Internal solitary waves in the Mozambique Channel: Observations and interpretation

This paper presents new results showing that the Sofala shelf in the Mozambique Channel (20°S, 36°E) is a previously unknown “hot spot” for the generation of internal tides and internal waves. We investigate available Envisat advanced synthetic aperture radar imagery of the region, which is capable of showing the surface signatures of the internal waves. This is complemented by modeling of the ray pathways of internal tidal energy propagation, and of the P. G. Baines (1982) barotropic body force, which drives the generation of internal tides near the shelf break. The hot spot region is localized between 20° and 21°S because of the particular nature of the bathymetry there. Farther north and south, the forcing is reduced and insufficient to generate internal solitary waves in the synthetic aperture radar images. The analysis reveals two distinct types of internal wave trains that are observed traveling oceanward away from the shelf break, and we suggest that these result from direct generation at the shelf break and from “local” generation at about 80 km from the shelf break, respectively, because of the surfacing of internal tidal rays at the thermocline. Finally, we have investigated seasonal differences in the wave patterns, which penetrate more extensively into the channel during the southern summer and appear slightly farther to the south during the southern winter. We also conclude that the local generation process is more likely to occur during the winter when the stratification is reduced. <br/