Dispersion relations of Nambu-Goldstone modes at finite temperature and density
arXiv:1406.6271 · doi:10.1103/PhysRevD.91.056006
Abstract
We discuss the dispersion relations of Nambu-Goldstone (NG) modes associated with spontaneous breaking of internal symmetries at finite temperature and/or density. We show that the dispersion relations of type-A (I) and type-B (II) NG modes are linear and quadratic in momentum, whose imaginary parts are quadratic and quartic, respectively. In both cases, the real parts of the dispersion relations are larger than the imaginary parts when the momentum is small, so that the NG modes can propagate far away. We derive the gap formula for NG modes in the presence of a small explicit breaking term. We also discuss the gapped partners of type-B NG modes, when type-A and type-B NG modes coexist.
32 pages, no figure; typos corrected, some discussions elaborated in Sec. VB5
References in corpus (8)
- Counting rule for Nambu-Goldstone modes in nonrelativistic systems
- A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density
- Counting rule of Nambu-Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach
- Nambu-Goldstone bosons with fractional-power dispersion relations
- Effective Lagrangians for quantum many-body systems
- Spontaneously Broken Gauge Theories and the Coset Construction
- Nambu-Goldstone bosons and the Higgs mechanism without Lorentz invariance: Analysis based on constrained-system theory
- Topological interactions of Nambu-Goldstone bosons in quantum many-body systems
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- Geometry of Classical Nambu-Goldstone Fields
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