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

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