A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density

Abstract

We adapt the Goldstone theorem to study spontaneous symmetry breaking in relativistic theo- ries 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. We find that that the latter interpolate gapped excitations. In contrast, all existing versions of the Goldstone theorem predict the existence of gapless modes. We derive exact non-perturbative expressions for their gaps, in terms of the chemical potential and of the symmetry algebra.

arXiv comment5 pages. v2: minor modifications, matches the PRL version

References in corpus (6)

• Kaon Condensation and Goldstone's Theorem
• Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems
• On the number of Nambu-Goldstone bosons and its relation to charge densities
• Spontaneous Symmetry Breaking with Abnormal Number of Nambu-Goldstone Bosons and Kaon Condensate
• Low-Energy Quantum Effective Action for Relativistic Superfluids
• Spontaneous Symmetry Probing

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