Anomalous dimensions for the nonlinear sigma-model in 2+ε dimensions. Pt. 1

The anomalous dimensions of composite scaling operators without spatial derivations are given for the G(m1+m2)/G(m1) . G(m2) matrix models (G=O,U,Sp) in a 2+ε expansion in four-loop order. They are expressed in the expansion coefficients in the transversal components of the operators invariant under G(m1) . G(m2). In contrast to the three-loop order result the dimensions are no longer proportional to the first expansion coefficient. Special cases discussed are the operators of the O(n)-vector model, the CPn-1 model, and the HPn-1 model. The ξ-function of the O(n) model contributes a piece to the comparison of the 1/n and ε-expansions of the exponent η which allows the determination of the unknown coefficient B1 of Hikami's four-loop β-function (Bernreuther and Wegner). (orig.)