Double expansion in asymptotically free theories

I propose an approximation scheme for asymptotically free field theories combining both weak coupling and strong coupling series. The weak coupling expansion is used to integrate the high frequency modes and the resulting low energy effective theory is solved using the strong coupling expansion. In some models there exists an intermediate scale at which both expansions make sense. The method is tested on few low dimensional models for which an exact solution is known.Comment: 15 pages, written in LaTeX, figures generated using FEYNMANN are commented and can be obtained upon request

Decimation in more then one dimension

We develop a formalism for performing real space renormalization group transformations of the "decimation type" using perturbation theory. The type of transformations beyond $d=1$ is nontrivial even for free theories. We check the formalism on solvable case of $O(N)$ symmetric Heisenberg chain. The transformation is particularly useful to study asymptotically free theories. Results for one class of such models, the d=2 O(N) symmetric $\sigma$ models ($N\ge 3$) for decimation with scale factor $\eta=2$ (when quarter of the points is left) are given as an example.Comment: 17 pages, latex, 3 diagrams using FEYNMA

Electron Structure Near Abrupt Edges in 2DEG under Strong Magnetic Field

Energies and wave functions of edge states in twodimensional electron gas are evaluated for a finite step potential barrier model. The spectrum, instead of smooth bending of Landau branches in the vicinity of the barrier acquires a steplike form; unexpected edge plateaus and significant energy gap reduction take place between the neighbouring Landau branches above the barrier tops. The origin of these phenomena is traced. Stability with respect to modifications is established. Manifestation of the qualitatively new features of electron densities of states in abrupt confinements through magnetooptical and nuclear magnetic spin relaxation effects is proposed.Comment: 24 pages in LATEX, 7 figures available on request, to appear in physica status solidi(b

Majorana states in a p-wave superconducting ring

The spectrum of excitations of the chiral superconducting ring with internal and external radii, comparable with coherence length, trapping a unit flux is calculated. We find within the Bogoliubov-deGennes approach that there exists a pair of precisely zero energy states. They are not protected by topology, but are stable under certain deformations of the system. We discuss the ways to tune the system so that it grows into such a "Majorana disk". This condition has a character of a resonance phenomenon

Amplitude Zeroes in Collinear Processes or What Is Left from a Factorizable 2d Model in Higher Dimensions

We show that for collinear processes, i.e. processes where the incoming and outgoing momenta are aligned along the same line, the S-matrix of the tree level 2+1 dimensional Thirring model factorizes: any S - matrix element is a product of $2\rightarrow 2$ elements. In particular this means nullification of all collinear $2 \rightarrow n$ amplitudes for $n > 2$.Comment: latex , 8 pp., 2 fig. not include