PERTURBATION-THEORY AND GOLDSTONE SINGULARITIES IN THE ORDERED PHASE OF THE O-N-SYMMETRICAL PHI(4) THEORY IN A HALF-SPACE

The O-n-symmetric Phi(4) theory in a half-space is investigated. The propagators of the theory in the ordered phase for zero external field are obtained, and the dependence of these propagators on the boundary conditions is studied. The general form of the Goldstone asymptotics of the various correlation functions, as functions of weak external fields and small momenta and large distances from the boundary of the system, is determined.