Goldstone theorem revisited
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.
Keywords
Cite
@article{arxiv.1404.5619,
title = {Goldstone theorem revisited},
author = {Alexander Kartavtsev},
journal= {arXiv preprint arXiv:1404.5619},
year = {2014}
}
Comments
This paper has been withdrawn by the author because the operator sigma used in the analysis is not defined as well as has discontinuities at parts of the field space and thus the expectation value of its commutator with the current operator is not well defined