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Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance

Haruki Watanabe and Hitoshi Murayama
Phys. Rev. Lett. 108, 251602 – Published 21 June 2012
Physics logo See Synopsis: Counting Broken Symmetries

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.

  • Received 3 March 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.251602

© 2012 American Physical Society

Synopsis

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Counting Broken Symmetries

Published 21 June 2012

Theorists obtain a general theorem that predicts the number of Goldstone modes generated by spontaneous symmetry breaking in nonrelativistic systems.

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Authors & Affiliations

Haruki Watanabe1,2,* and Hitoshi Murayama1,3,4,†

  • 1Department of Physics, University of California, Berkeley, California 94720, USA
  • 2Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
  • 3Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 4Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes for Advanced Study, University of Tokyo, Kashiwa 277-8583, Japan

  • *hwatanabe@berkeley.edu
  • hitoshi@berkeley.edu, hitoshi.murayama@ipmu.jp

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Issue

Vol. 108, Iss. 25 — 22 June 2012

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