A consistent hamiltonian treatment of the Thirring-Wess and Schwinger model in the covariant gauge

We present a unified hamiltonian treatment of the massless Schwinger model in the Landau gauge and of its non-gauge counterpart–the Thirring-Wess (TW) model. The operator solution of the Dirac equation has the same structure in the both models and identifies free fields as the true dynamical degrees of freedom. The coupled boson field equations (Maxwell and Proca, respectively) can also be solved exactly. The Hamiltonan in Fock representation is derived for the TW model and its diagonalization via a Bogoliubov transformation is suggested. The axial anomaly is derived in both models directly from the operator solution using a hermitian version of the point-splitting regularization. A subtlety of the residual gauge freedom in the covariant gauge is shown to modify the usual definition of the “gauge-invariant” currents. The consequence is that the axial anomaly and the boson mass generation are restricted to the zero-mode sector only. Finally, we discuss quantization of the unphysical gauge-field components in terms of ghost modes in an indefinite-metric space and sketch the next steps within the finite-volume treatment necessary to fully reveal physical content of the model in our hamiltonian formulation.