Scalar field theory on κ\kappa-Minkowski space-time and Doubly Special Relativity

In this paper we recall the construction of scalar field action on $\kappa$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $\kappa$-Poincar\'e algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space-time, equivalent to the original one. Adding the self-interaction $\Phi^4$ term we investigate the modified conservation laws. We show that the local interactions on $\kappa$-Minkowski space-time give rise to 6 inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.Comment: 17 pages; some editing done, final version to be published in Int. J. Mod. Phys.

Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three

We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [C] and [CM2], this leads to the full classification of three-dimensional Lorentzian g.o. spaces and naturally reductive spaces

Coherent states for the q-deformed quantum mechanics on a circle

The q-deformed coherent states for a quantum particle on a circle are introduced and their properties investigated.Comment: 11 pages, 2 PostScript figure

Three-dimensional laser window formation for industrial application

The NASA Lewis Research Center has developed and implemented a unique process for forming flawless three-dimensional, compound-curvature laser windows to extreme accuracies. These windows represent an integral component of specialized nonintrusive laser data acquisition systems that are used in a variety of compressor and turbine research testing facilities. These windows are molded to the flow surface profile of turbine and compressor casings and are required to withstand extremely high pressures and temperatures. This method of glass formation could also be used to form compound-curvature mirrors that would require little polishing and for a variety of industrial applications, including research view ports for testing devices and view ports for factory machines with compound-curvature casings. Currently, sodium-alumino-silicate glass is recommended for three-dimensional laser windows because of its high strength due to chemical strengthening and its optical clarity. This paper discusses the main aspects of three-dimensional laser window formation. It focuses on the unique methodology and the peculiarities that are associated with the formation of these windows

Coherent states of a charged particle in a uniform magnetic field

The coherent states are constructed for a charged particle in a uniform magnetic field based on coherent states for the circular motion which have recently been introduced by the authors.Comment: 2 eps figure

On the definition of velocity in doubly special relativity theories

We discuss the definition of particle velocity in doubly relativity theories. The general formula relating velocity and four-momentum of particle is given.Comment: 7 page

Field theory on κ\kappa--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry

This paper is devoted to detailed investigations of free scalar field theory on $\kappa$-Minkowski space. After reviewing necessary mathematical tools we discuss in depth the Lagrangian and solutions of field equations. We analyze the spacetime symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetry. We show that the version of the theory usually studied breaks Lorentz invariance in a subtle way: There is an additional trans-Planckian mode present, and an associated conserved charge (the number of such modes) is not a Lorentz scalar.Comment: 22 pages, 1 figure, formulas in sect. III correcte