Goldstone theorem revisited

TL;DR

This paper revisits the Goldstone theorem, identifying a loophole in its proof and discussing conditions under which excitations are massless or nearly massless, challenging traditional assumptions.

Contribution

It uncovers a loophole in the current-algebra proof of the Goldstone theorem and explores the mass behavior of excitations in models with large vacuum expectation values.

Findings

Loophole identified in the proof of Goldstone theorem

Mass of tangential excitations can approach zero without spontaneous symmetry breaking

Excitations can be nearly massless even when symmetry is not spontaneously broken

Abstract

According to the Goldstone theorem a scalar theory with a spontaneously broken global symmetry contains strictly massless states. In this letter we identify a loophole in the current-algebra proof of the theorem. Therefore, the question whether in models with Mexican hat potential the tangential excitations are strictly massless or are just almost massless as compared to the radial ones remains open. We also argue that mass of the tangential excitations approaches zero even if the symmetry is not spontaneously broken but a combination of the field components invariant under the symmetry transformations acquires a large vacuum expectation value.