A relativistic superalgebra in a generalized Schroedinger picture

We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive relativistic particles with spin zero and spin-1/2 are expressed in terms of the principal series of the unitary representations of the Lorentz group. We also consider the massless case. New Hamilton operators are conctructed for the massless particles with spin zero and spin 1/2.Comment: 7 page

The possibilities of developing new industrial markets for farm products

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One particle quantum equation in a de Sitter spacetime

We consider a free particle in a de Sitter spacetime. We use a picture in which the analogs of the Schr\"odinger operators of the particle are independent of both the time and the space coordinates. These operators induce operators which are related to Killing vectors of the de Sitter spacetime.Comment: 12 page

Test of Conformal Invariance in One-Dimensional Quantum Liquid with Long-Range Interaction

We numerically study the momentum distribution of one-dimensional Bose and Fermi systems with long-range interaction $g/r^2$ for the ``special'' values $g= -\frac{1}{2}, 0, 4$, singled out by random matrix theory. The critical exponents are shown to be independent of density and in excellent agreement with estimates obtained from $c=1$ conformal finite-size scaling analysis.Comment: 25 page

Numerical investigations of scaling at the Anderson transition

At low temperature T, a significant difference between the behavior of crystals on the one hand and disordered solids on the other is seen: sufficiently strong disorder can give rise to a transition of the transport properties from conducting behavior with finite resistance R to insulating behavior with R=infinity as T -> 0. This well-studied phenomenon is called the disorder-driven metal-insulator transition and it is characteristic to non-crystalline solids. In this review of recent advances, we have presented results of transport studies in disordered systems, ranging from modifications of the standard Anderson model of localization to effects of a two-body interaction. Of paramount importance in these studies was always the highest possible accuracy of the raw data combined with the careful subsequent application of the finite-size scaling technique. In fact, it is this scaling method that has allowed numerical studies to move beyond simple extrapolations and reliably construct estimates of quantities as if one were studying an infinite system.Comment: 18 pages, 6 figures, "The Anderson Transition and its Ramifications-Localisation, Quantum Interference, and Interactions", 'Lecture Notes in Physics' series, ed. T. Brandes and S. Kettemann, Springer Verlag, to be publishe