Ward-Takahashi relation at finite temperature in Bose-Einstein condensation of trapped neutral atoms

Masahiko Okumura, Yoshiya Yamanaka

    Research output: Contribution to journalArticle

    5 Citations (Scopus)


    We prove that the Ward-Takahashi relations at finite temperature are satisfied at the tree level for a system of a trapped Bose-Einstein condensate when the zero mode is included in the quasi-particle picture properly. This implies that the zero mode represents the Nambu-Goldstone mode and that it is introduced in a way consistent with the Goldstone theorem. In the proof, we employ thermo field dynamics which is a real-time operator formalism of quantum field theory at finite temperature.

    Original languageEnglish
    Pages (from-to)157-172
    Number of pages16
    JournalPhysica A: Statistical Mechanics and its Applications
    Publication statusPublished - 2005 Mar 15



    • Bose-Einstein condensation
    • Thermo field dynamics
    • Ward-Takahashi relation

    ASJC Scopus subject areas

    • Mathematical Physics
    • Statistical and Nonlinear Physics

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