Field theory anomalies involving the energy-momentum tensor

Abstract

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.