Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance

We address the well-known problem that Nambu-Goldstone's theorem does not correctly predict the number of Nambu-Goldstone bosons in systems without Lorentz invariance. Using the effective Lagrangian approach, we provide a general prescription to predict the number of Nambu-Goldstone bosons and the form of their dispersion relation correctly. We trace the abnormalities in non-Lorentz invariant systems back to Nambu-Goldstone boson pairs becoming canonically conjugate--this reduces the number of Nambu-Goldstone bosons and changes the linear dispersions to quadratic. The generality of our construction clarifies the powerful approach of analyzing quantum many-body systems--including strongly coupled systems--by their symmetry breaking patterns. This will also aid our understanding of recent experiments and theoretical works on spinor BECs and lattices of topological defects. Reference: H. Watanabe, H. Murayama, PRL 108, 251602 (2012)