An extension of Anderson-Higgs mechanism

When free vortices are present in the pseudogap region of underdoped cuprates, it is shown that conventional Anderson-Higgs mechanism does not work because the Goldstone field is not an analytic function. However, after decomposing the Goldstone field into longitudinal and transverse components, we find that the former can be eliminated by a special gauge transformation and the gauge field becomes massive, but the latter persists in the theory in any case. Thus we obtain an extended Anderson-Higgs mechanism which exhibits completely new physics comparing with the conventional one.