Field theory anomalies involving the energy-momentum tensor

Generalized Ward-Takahashi identities (WTI's) of the energymomentum tensor in a free spinor field theory with SU(3) currents were analyzed for possible non-canonical behavior (anomalies). The WTI's, derived by a functional integration technique, are the divergence equations for the axial-vector, vector, and tensor currents in n-point functions (n-pf's), i.e. Green's functions, involving the energy-momen tum tensor and all possible combinations of vector, axial-vector, scalar, and pseudo-scalar external currents (V, A, S, and P). In addition the trace identities (Tl) of the n-pf's involving the energymomentum tensor were investigated. The WTI's and trace identities were first checked by naive manip ulation of single loop Feynman diagrams, (i.e. ignoring divergences and surface terms in shifts of integration variables). Then defining "physical" amplitudes in terms of a Pauli-Villars type regularization and a self-consistent renormalization scheme (by addition of polynomial counterterms), possible anomalies of the WTI's and Tl were defined. As a result of the regularization, 1/m-terms of n-pf's having a coef ficient m in the axial-vector WTl and the trace identity were found to contribute to posssbls anornalisso Using ths couritsrteriTiS in a selfconsistent manner, it was found that all the tensor and vector WTI's could be satisfied (thus satisfying Poincare and gauge invariance, respectively), while anomalies were found in the axial-vector WTl and trace identity.