LIGHT-FRONT QUANTIZED SCHWINGER MODEL AND θ-VACUA

The light-front (LF) quantization of the bosonized Schwinger model is discussed. The proposal, successfully used earlier for describing the spontaneous symmetry breaking (SSB) on the LF, of separating first the scalar field into the dynamical condensate and the fluctuation fields before employing the standard Dirac method works here as well. The condensate variable is now shown to be a q-number operator in contrast to the case of SSB where it was shown to be a c-number. The condensate or θ-vacua emerge straightforwardly along with their continuum normalization which avoids the violation of the cluster decomposition property. Attention is drawn to the fact that the theory quantized, say, at equal x+, carries in it at the same time information on equal x- commutators as well.