Conformal anomaly in the two-dimensional nonlinear σ model

Abstract

The conformal anomaly of the nonlinear \ensuremath{\sigma} model is investigated by the canonical quantization method. The relations built among the components of the energy-momentum tensor are discussed with the standard quantum field theory argumentation. A more general structure for the canonical quantization is furnished by considering the freedom of redefining the field variables in the Hamiltonian formalism. Special attention is paid to the analysis of the so-called Schwinger terms defined as anomalous terms generated at the quantum level. The conformal anomaly can be obtained by virtue of various conservation rules without preimposing reparametrization invariance. Our results not only coincide with the ones obtained from the \ensuremath{\beta}-functional approach to the two-loop level but also illustrate the transformation properties for the field configurations in terms of the so-called improvement terms. While it is more natural to deal with the canonical energy-momentum tensor than the usual stress-energy tensor, the difference between both is clarified. With extra consideration of the dilaton coupling, we furthermore show that the distinction between these two energy-momentum tensors is obvious. In addition, the dilaton effect on the conformal anomaly can be obtained with no reference to its explicit coupling pattern in the action.