Alberto Nicolis, Federico Piazza
We adapt the Goldstone theorem to study spontaneous symmetry breaking in relativistic theories at finite charge density. It is customary to treat systems at finite density via non-relativistic Hamiltonians. Here we highlight the importance of the underlying relativistic dynamics. This leads to seemingly new results whenever the charge in question is spontaneously broken and does not commute with other broken charges. These would normally be associated with gapless Goldstone excitations. We find that, in fact, their currents interpolate gapped excitations. We derive exact non-perturbative expressions for their gaps, in terms of the chemical potential and of the symmetry algebra.
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http://arxiv.org/abs/1204.1570
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