2014/02/28 by Haruki Watanabe, Hitoshi Murayama · 3 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Gauge symmetry #Gauge theory #Inverse problem for Lagrangian mechanics #Lagrangian #Numerical methods for differential equations #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Statistical physics #Theoretical physics #cond-mat.other #cond-mat.quant-gas #cond-mat.str-el #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevx.4.031057
published as Phys. Rev. X 4, 031057 (2014) · 34 pages, 5 tables, 2 figures; v2: published version (to appear in Physical Review X)
arxiv created 2014/09/19 · openalex publication_date 2014/09/29 · arxiv updated 2014/09/30 · openalex created_date 2021/02/01 · openalex updated_date 2026/08/06
The effective Lagrangian for Nambu-Goldstone bosons (NGBs) in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing 1 dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in 1 1 dimensions.