The Linear Sigma-Model in the 1/N-Expansion via Dynamical Boson Mappings and Applications to $ππ$-Scattering

Abstract

We present a non-perturbative method for the study of the O(N+1)-version of the linear sigma-model. Using boson-mapping techniques, in close analogy to those well-known for fermionic systems, we obtain a systematic 1/N-expansion for the Hamiltonian which is symmetry-conserving order by order. The leading order for the Hamiltonian is evaluated explicitly and we apply the method to $ππ$-scattering, in deriving the T-matrix to leading order.

28 pages, Latex, (with minor corrections to some misprints in the appendix of the old version)