Gauged nonlinear sigma model in light-front frame: Hamiltonian and BRST formulations (Q5950649)

The paper considers the problem of setting up the Hamiltonian formalism and subsequent quantization of the one-dimensional sigma-model, i.e., a system of relativistic-invariant wave equations for a multicomponent vector field, the local length of the vector being fixed \(\equiv 1\). Additionally, the sigma-field is coupled to the corresponding gauge fields. The field equations are written in the light-cone variables. It is known that the introduction of the Hamiltonian formalism makes it necessary to fix the gauge, therefore the system loses its gauge invariance. On the other hand, the gauge invariance must be present, for a consistency of the quantization procedure. The problem is resolved by means of the the so-called BRST formalism, which adds to the usual commuting variables additional anticommuting (Grassmann's) ones, which makes it possible to restore, effectively, the gauge invariance, despite the fixed gauge, and thus perform the quantization procedure in a consistent form. In the present work, the BRST procedure is implemented for the gauged nonlinear sigma-model.