Manifestly covariant approach for the one-soliton sector

Abstract

The one-loop contributions to the meson propagator and to the meson-soliton scattering amplitude in the one-soliton sector are analyzed using ordinary Feynman rules. It is found that, at the level of the propagator, the most severe infrared divergences cancel out while others remain. The structure of the remaining divergences is studied. We conclude that, among other things, the coefficient function of the leading divergence only depends upon the classical soliton solution. An extended Lehmann-Symanzik- Ziminerman reduction technique, to work in the one-soliton sector, is proposed. Then, it is shown thht, under certain mathematical assumptions, the above-mentioned S-matrix element turns out to be free of zeromode singularities.