Wilson's Operator Expansion: Can It Fail

摘要

The status of operator product expansion (OPE) in the presence of nonperturbative effects is discussed within the framework of some simple 4d Higgs model, 2d sigma-model and Schwinger model. The general formulation of OPE is presented and it is demonstrated that there exists a consistent procedure allowing one to define unambiguously both coefficient functions and matrix elements of composite operators. One of the key elements of the procedure is introduction of an auxiliary parameter, the normalization point mu . The two extremes considered are lambda phi exp 4 theory with no spontaneous breaking of the symmetry and the O(N) sigma model in the limit N implies infinity. In the former case there is only perturbative contribution to (phi exp 2 ) while in the latter case the perturbative pieces are suppressed by 1/N factors. Numerically QCD is much closer to the O(N) sigma model in the large N limit. Comments on specific features of QCD are presented. (Atomindex citation 16:055147)