Operator solution of the light-front Thirring-Wess model

Abstract

We present an operator solution of the Thirring-Wess model, formulated and quantized in terms of light-front (LF) variables. The model describes a system of massless fermions interacting with massive vector bosons in two space-time dimensions. An important ingredient of the solution is a consistent quantization of the two-dimensional massless LF fermion field. The field equations are solved exactly on an operator level and the quantum LF Hamiltonian is derived in terms of independent field variables. The axial anomaly and the interacting correlation functions are computed nonperturbatively from the operator solution. An analogous operator solution in the conventional field theory is briefly described for comparison. While in the LF case the ``empty'' Fock vacuum is the lowest-energy eigenstate of the full Hamiltonian, the corresponding Hamiltonian in the conventional theory has to be diagonalized in order to find the true physical ground state, which is a dynamical state with a complicated structure. A comment concerning a recently discussed equivalence between the LF and conventional form of field theory concludes the paper.