Interpolating relativistic and non-relativistic Nambu-Goldstone and Higgs modes

Abstract

When a continuous symmetry is spontaneously broken in non-relativistic theories, there appear Nambu-Goldstone (NG) modes, whose dispersion relations are either linear (type-I) or quadratic (type-II). We give a general framework to interpolate between relativistic and non-relativistic NG modes, revealing a nature of type-I and II NG modes in non-relativistic theories. The interpolating Lagrangians have the nonlinear Lorentz invariance which reduces to the Galilei or Schrodinger invariance in the non-relativistic limit. We find that type-I and type-II NG modes in the interpolating region are accompanied with a Higgs mode and a chiral NG partner, respectively, both of which are gapful. In the ultra-relativistic limit, a set of a type-I NG mode and its Higgs partner remains, while a set of type-II NG mode and gapful NG partner turns to a set of two type-I NG modes. In the non-relativistic limit, the both types of accompanied gapful modes become infinitely massive, disappearing from the spectrum. The examples contain a phonon in Bose-Einstein condensates, a magnon in ferromagnets, and a Kelvon and dilaton-magnon localized around a skyrmion line in ferromagnets.

20 pages, no figure

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Cited by in corpus (8)

• An Introduction to Spontaneous Symmetry Breaking
• Conformal symmetry of trapped Bose-Einstein condensates and massive Nambu-Goldstone modes
• Fano resonance through Higgs bound states in tunneling of Nambu-Goldstone modes
• Exact Ground States and Domain Walls in One Dimensional Chiral Magnets
• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Effective field theory of magnon: Dynamics in chiral magnets and Schwinger mechanism
• Stability and Absence of a Tower of States in Ferrimagnets
• Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes