DYNAMIC CHARGES IN FIELD-THEORIES

The origin of trace coefficients lies in the classical dynamics of perfect or separable systems in one space, one time dimension. However the notion of systems of conserved integrals of the motion carries over to space dimensions of arbitrary degree. Physically, they arise as coefficients in an asymptotic expansion for the partition function for a model gas at high temperature. The integrals are charges in the system that are dynamic and conserved. In some σ models, in one dimension, a non-local dynamic charg e exists which controls the quantum system. The striking similarity between σ models in one space dimension and non-Abelian gauge models suggests they exist there also. In this paper we develop efficient functional techniques for finding dynamic charges in any dimension. One method depends on a path integral representation for the partition function, the other on a contour integral representation for it. © 1979.