Goldstone theorem, Hugenholtz-Pines theorem, and Ward-Takahashi relation in finite volume Bose-Einstein condensed gases

Hiroaki Enomoto, Masahiko Okumura, Yoshiya Yamanaka

Research output: Contribution to journalArticle

6 Citations (Scopus)


We construct an approximate scheme based on the concept of the spontaneous symmetry breakdown, satisfying the Goldstone theorem, for finite volume Bose-Einstein condensed gases in both zero and finite temperature cases. In this paper, we discuss the Bose-Einstein condensation in a box with periodic boundary condition and do not assume the thermodynamic limit. When energy spectrum is discrete, we found that it is necessary to deal with the Nambu-Goldstone mode explicitly without the Bogoliubov's prescription, in which zero-mode creation- and annihilation-operators are replaced with a c-number by hand, for satisfying the Goldstone theorem. Furthermore, we confirm that the unitarily inequivalence of vacua in the spontaneous symmetry breakdown is true for the finite volume system.

Original languageEnglish
Pages (from-to)1892-1917
Number of pages26
JournalAnnals of Physics
Issue number8
Publication statusPublished - 2006 Aug 1



  • Bose-Einstein condensation
  • Goldstone theorem
  • Hugenholtz-Pines theorem
  • Spontaneous symmetry breakdown
  • Unitarily inequivalent vacua
  • Ward-Takahashi relations

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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