Currents and energy-momentum tensor in the chiral Schwinger model with general vector and axial-vector couplings.

Abstract

Using the point-splitting procedure and the method of functional integration, we define currents in the chiral Schwinger model and compute the correlation funtions of currents with themselves and with the fundamental fields. We show that the ambiguities in the choice of the phase factor employed in the point-splitting procedure can be compensated by mixing of the currents with the gauge potential ${\mathit{A}}_{\mathrm{\ensuremath{\mu}}}$ and ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}$${\mathit{A}}^{\ensuremath{\nu}}$. A three-parameter family of conserved currents is found and the transformations they generate are identified. In order to construct the conserved energy-momentum tensor, it is necessary to allow for mixings with ${\mathit{A}}_{\mathrm{\ensuremath{\mu}}}$${\mathit{A}}_{\ensuremath{\nu}}$ and ${\mathit{g}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}$${\mathit{A}}_{\mathrm{\ensuremath{\alpha}}}$${\mathit{A}}^{\mathrm{\ensuremath{\alpha}}}$. We compute the two-point function of the energy-momentum tensor and the correlation functions of it with the fundamental fields. The physics of the chiral model is discussed in comparison with the vector model.