The paper is devoted to the spherically symmetric problem of General Relativity. Existing solutions obtained by K. Schwarzschild and V. Fock are presented discussed. A special geometry Riemannian space induced gravitation proposed. According this four-dimensional assumed be Euclidean with respect coordinates time coordinate. solution Einstein equations for empty coincides in Gullstand-Painlever...

We study the large N reduced model of D-dimensional Yang-Mills theory with special attention to dynamical aspects related to the eigenvalues of the N×N matrices, which correspond to the space-time coordinates in the IIB matrix model. We first put an upper bound on the extent of space time by perturbative arguments. We perform a Monte Carlo simulation and show that the upper bound is actually sa...

The chief difficulty with the parallel coordinates visualization technique is that large data sets become difficult to read due to cluttering of the data. Many techniques have been proposed and implemented to address this problem. A non-algorithmic solution is to simply display the visualization with a larger physical display area. However, a straightforward implementation of this approach may ...

We construct field theory on noncommutative κ-Minkowski spacetime. Having the Lorentz action on the noncommutative space-time coordinates we show that the field lagrangian is invariant. We show that noncommutativity requires replacing the Leibnitz rule with the coproduct one.

We describe some recent progress in our understanding of Yang-Mills theories formulated on noncommutative spaces and in particular how to formulate the standard model on such spaces The idea that space-time might be noncommutative at short distances is not new but it was taken very seriously recently because noncommutative coordinates were found in a specific limit of string theory. This is nev...

The AdS/CFT transformation relates two nonlinear realizations of (super)conformal groups: their realization in the appropriate field theories in Minkowski space with a Goldstone dilaton field and their realization as (super)isometry groups of AdS (super)spaces. It exists already at the classical level and maps the field variables and space-time coordinates of the given (super)conformal field th...

We discuss properties of conformal geodesics on general, vacuum, and warped product space-times and derive a system of conformal deviation equations. The results are used to show how to construct on the Schwarzschild-Kruskal space-time global conformal Gauss coordinates which extends smoothly and without degeneracy to future and past null infinity.

In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...