Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance

2012/03/31 by Haruki Watanabe, Hitoshi Murayama · 1 voice · 13 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Chromodynamics and Particle Interactions #cond-mat.other #hep-ph #hep-th

paper · pdf · doi:10.1103/physrevlett.108.251602

published as Phys. Rev. Lett. 108, 251602 (2012) · 5 pages, REVTeX 4.1; v3: published version

arxiv created 2012/06/12 · openalex publication_date 2012/06/21 · arxiv updated 2014/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

Using the effective Lagrangian approach, we clarify general issues about Nambu-Goldstone bosons without Lorentz invariance. We show how to count their number and study their dispersion relations. Their number is less than the number of broken generators when some of them form canonically conjugate pairs. The pairing occurs when the generators have a nonzero expectation value of their commutator. For non-semi-simple algebras, central extensions are possible. The underlying geometry of the coset space in general is partially symplectic.

Citations

• Global aspects of current algebra
• Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I
• Field theories with « Superconductor » solutions
• Kaon condensation and Goldstone's theorem
• Structure of Phenomenological Lagrangians. I
• Broken Symmetries

Cited by

• Effective Lagrangian for Nonrelativistic Systems
• Symmetry breaking in holographic theories with Lifshitz scaling
• Possibility of ferromagnetic neutron matter
• Emergence of the Unconventional Type-II Nambu-Goldstone Modes with Topological Origin in Bose Superfluids
• Conformal symmetry of trapped Bose-Einstein condensates and massive Nambu-Goldstone modes
• Antiferromagnetic magnons and local anisotropy: dynamical mean-field study
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes
• Theory of collective magnetophonon resonance and melting of a field-induced Wigner solid
• Nambu-Goldstone modes propagating along topological defects: Kelvin and ripple modes from small to large systems
• Exceptional nonrelativistic effective field theories with enhanced symmetries
• Nonrelativistic Banks-Casher relation and random matrix theory for multicomponent fermionic superfluids
• Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics

Discussions

• Your text reviews the standard Lorentz-symmetric case for particle physics. Illustrate it with, e.g. $\phi=(\phi_1,\phi_2,\phi_3)$ , so the three generators of SO(3) mix its three components. If your [stackexchange, 0 points]

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