Fermion Condensate and the Spectrum of Massive Schwinger Model in Bogoliubov Transformed Vacuum

Abstract

We calculate the spectrum of the charge zero sector in two-dimensional quantum electrodynamics (massive Schwinger model). The calculations are first done in the rest frame with the perturbative vacuum within q q and qq q q subspaces. This leads to the infrared instability at small fermion mass. Then, we make the Bogoliubov transformation of the vacuum. There, it is found that the quasi-particle q q states achieve a remarkably good description of the boson mass spectrum. At small fermion mass ( m 0 ≤ 0.l (g/√π)), the Bogoliubov transformed state predicts the boson mass which agrees with the analytic estimation and thus is better than that calculated by the discretized light cone quantization methods at the same level of matrix dimensions. The fermion condensate of the vacuum is also estimated as the function of the fermion mass. At the massless limit, we reproduce the right condensate value as obtained analytically in the continuum limit.