Towards a constructive approach of a gauge invariant, massiveP(φ)2 theory

Abstract

As part of a possible constructive approach to a gauge invariantP(φ)2 theory, we consider massive, scalar, polynomially selfcoupled fields φ in a fixed external Yang-Mills potentialA in two-dimensional euclidean space. For a large class ofA's we show that the corresponding euclidean Green's functions for the fields φ have a lower mass gap for weak coupling which is uniform inA. The result is obtained by adapting the Glimm-Jaffe-Spencer cluster expansion to the present situation through Kato's inequality, which reflects the diamagnetic effect of the Yang-Mills potential. A discussion of the corresponding gauge covariance is included.