Theta-Vacua in the Light-Front Quantized Schwinger Model

TL;DR

This paper explores the light-front quantization of the bosonized Schwinger model, demonstrating the emergence of Theta-vacua as operator-valued condensates that preserve continuum normalization and cluster decomposition.

Contribution

It introduces a novel approach to LF quantization of the Schwinger model, showing condensates as q-number operators and deriving Theta-vacua without violating cluster properties.

Findings

Theta-vacua emerge as operator condensates.

The continuum normalization is maintained.

The approach avoids cluster decomposition violations.

Abstract

The light-front (LF) quantization of the bosonized Schwinger model is discussed in the "continuum formulation". 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, however, 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 or a background field. The "condensate or Theta-vacua" emerge straightforwardly together with their continuum normalization which avoids the violation of the cluster decomposition property in the theory. Some topics on the "front form" theory are summarized in the Appendices and attention is drawn to the fact that "the theory quantized, say, at equal $x^{+}$ seems already to carry information on equal $x^{-}$ commutators as well".