Goldstone bosons in the massless Thirring model. Witten's criterion

TL;DR

This paper demonstrates that the free massless scalar field in the chirally broken phase of the massless Thirring model meets Witten's criterion, confirming its interpretation as a Goldstone boson through analysis of Ward identities and low-energy theorems.

Contribution

It provides a detailed analysis connecting Witten's criterion with the bosonization of the massless Thirring model, confirming the Goldstone nature of the scalar quanta.

Findings

The scalar field satisfies Witten's criterion for Goldstone bosons.

The ground state wave function's non-invariance is confirmed.

Ward identities support the Goldstone boson interpretation.

Abstract

We discuss the Ward identity and the low-energy theorem for the divergence of the axial-vector current in the massless Thirring model with fermion fields quantized in the chirally broken phase (Eur. Phys. J. C20, 723 (2001)). The Ward identity and the low-energy theorem are analysed in connection with Witten's criterion for Goldstone bosons (Nucl. Phys. B145, 110 (1978)). We show that the free massless (pseudo)scalar field bosonizing the massless Thirring model in the chirally broken phase satisfies Witten's criterion to interpret quanta of this field as Goldstone bosons. As has been shown in hep-th/0210104 and hep-th/0212226, Goldstone's criterion, the non-invariance of the wave function of the ground state, is also fulfilled.