TMD PDFs in the Laguerre polynomial basis

We suggest the modified matching procedure for TMD PDF to the integrated PDF aimed to increase the amount of perturbative information in the TMD PDF expression. The procedure consists in the selection and usage of the non-minimal operator basis, which restricts the expansion to desired general behavior. The implication of OPE allows to systematic account of the higher order corrections. In the case of TMD PDF we assume the Gaussian behavior, which suggests Laguerre polynomial basis as the best for the convergence of OPE. We present the leading and next-to-leading expression of TMD PDF in this basis. The obtained perturbative expression for the TMD PDF is valid in the wide region of $b_T$ (we estimate this region as $b_T\lesssim 2-3$ GeV$^{-1}$ depending on $x$).Comment: 19 pages, 6 figures; corrected abstract, conclusion and various misprints; version submitted to JHE

Dynamic speckle - Interferometry of micro-displacements

The problem of the dynamics of speckles in the image plane of the object, caused by random movements of scattering centers is solved. We consider three cases: 1) during the observation the points move at random, but constant speeds, and 2) the relative displacement of any pair of points is a continuous random process, and 3) the motion of the centers is the sum of a deterministic movement and random displacement. For the cases 1) and 2) the characteristics of temporal and spectral autocorrelation function of the radiation intensity can be used for determining of individually and the average relative displacement of the centers, their dispersion and the relaxation time. For the case 3) is showed that under certain conditions, the optical signal contains a periodic component, the number of periods is proportional to the derivations of the deterministic displacements. The results of experiments conducted to test and application of theory are given. © 2012 American Institute of Physics

GL_q(N)-covariant braided differential bialgebras

We study a possibility to define the (braided) comultiplication for the GLq(N)-covariant differential complexes on some quantum spaces. We discover such `differential bialgebras' (and Hopf algebras) on the bosonic and fermionic quantum hyperplanes (with additive coproduct) and on the braided matrix algebra BMq(N) with both multiplicative and additive coproducts. The latter case is related (for N=2) to the q-Minkowski space and q-Poincare algebra.Comment: 7 page