Coherent states for a particle on a sphere

The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a particle on a circle discussed in Kowalski K {\em et al} 1996 {\em J. Phys. A} {\bf 29} 4149, we deal with a deformation of the classical phase space related with quantum fluctuations. The expectation values of the position and the angular momentum in the coherent states are regarded as the best possible approximation of the classical phase space. The correctness of the introduced coherent states is illustrated by an example of the rotator.Comment: LaTeX, 16 pages, 2 figure

An Analysis of Diffraction in Deep-Inelastic Scattering

We propose a simple parametrization for the deep-inelastic diffractive cross section. It contains the contribution of $q\bar{q}$ production to both the longitudinal and the transverse diffractive structure functions, and of the production of $q\bar{q}g$ final states from transverse photons. We start from the hard region and perform a suitable extrapolation into the soft region. We test our model on the 1994 ZEUS and H1 data, and confront it with the H1 conjecture of a singular gluon distribution.Comment: 24 pages, LaTeX, figures included using epsfi

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.

AdS--Maxwell superalgebra and supergravity

In this paper we derive the Anti de Sitter counterpart of the super-Maxwell algebra presented recently by Bonanos et.\ al. Then we gauge this algebra and derive the corresponding supergravity theory, which turns out to be described by the standard N=1 supergravity lagrangian, up to topological terms.Comment: 8 pages, in v2 reference adde

Near-UV absorption in very cool DA white dwarfs

The atmospheres of very cool, hydrogen-rich white dwarfs (Teff <6000 K) are challenging to models because of the increased complexity of the equation of state, chemical equilibrium, and opacity sources in a low-temperature, weakly ionized dense gas. In particular, many models that assume relatively simple models for the broadening of atomic levels and mostly ideal gas physics overestimate the flux in the blue part of their spectra. A solution to this problem that has met with some success is that additional opacity at short wavelengths comes for the extreme broadening of the Lyman alpha line of atomic H by collisions primarily with H2. For the purpose of validating this model more rigorously, we acquired Hubble Space Telescope STIS spectra of 8 very cool white dwarfs (5 DA and 3 DC stars). Combined with their known parallaxes, BVRIJHK and Spitzer IRAC photometry, we analyze their entire spectral energy distribution (from 0.24 to 9.3 micron) with a large grid of model atmospheres and synthetic spectra. We find that the red wing of the Lyman alpha line reproduces the rapidly decreasing near-UV flux of these very cool stars very well. We determine better constrained values of Teff and gravity as well as upper limits to the helium abundance in their atmospheres.Comment: 41 pages, 9 figures. Accepted for publication in the Ap

On the uncertainty relations and squeezed states for the quantum mechanics on a circle

The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in the context of the uncertainty relations.Comment: 4 figure

Velocity of particles in Doubly Special Relativity

Doubly Special Relativity (DSR) is a class of theories of relativistic motion with two observer-independent scales. We investigate the velocity of particles in DSR, defining velocity as the Poisson bracket of position with the appropriate hamiltonian, taking care of the non-trivial structure of the DSR phase space. We find the general expression for four-velocity, and we show further that the three-velocity of massless particles equals 1 for all DSR theories. The relation between the boost parameter and velocity is also clarified.Comment: 12 page