Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?

TL;DR

This paper challenges Coleman's theorem by demonstrating that the ground state energy density of the sine-Gordon model remains bounded from below even when the coupling constant exceeds 8 pi, suggesting the model's ground state exists in this regime.

Contribution

The paper provides a counterexample to Coleman's theorem, showing the energy density is bounded from below for beta^2 > 8 pi, which was previously thought to be impossible.

Findings

Energy density remains bounded for beta^2 > 8 pi

Implications for the existence of the quantum ground state

Reevaluation of Coleman's theorem in this context

Abstract

We discuss Coleman's theorem concerning the energy density of the ground state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975). According to this theorem the energy density of the ground state of the sine-Gordon model should be unbounded from below for coupling constants beta^2 > 8 pi. The consequence of this theorem would be the non-existence of the quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that the energy density of the ground state in the sine-Gordon model is bounded from below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and soliton-soliton scattering in the sine-Gordon model.