The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach

TL;DR

This paper investigates the (1+1)-dimensional massive sine-Gordon field theory using a Gaussian wave-functional approach, revealing asymmetric vacua, bound states, and confirming mass predictions for related models.

Contribution

It introduces a Gaussian wave-functional method to analyze the massive sine-Gordon model, uncovering asymmetric vacua and bound states, and validates mass predictions for the bosonic Schwinger model.

Findings

Asymmetric vacuum exists in certain parameter regions.

Two-particle bound states are present in the asymmetric vacuum.

Masses of bosonic states agree with perturbation results for small fermion mass.

Abstract

The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum of the field system is asymmetrical. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for a part of the aforementioned region. Besides, for the bosonic equivalent to the massive Schwinger model, the masses of the one boson and two-boson bound states agree with the recent second-order results of a fermion-mass perturbation calculation when the fermion mass is small.