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Goldstone Theorem, Hugenholtz-Pines Theorem and Ward-Takahashi Relation in Finite Volume Bose-Einstein Condensed Gases

Hiroaki Enomoto·Masahiko Okumura·Yoshiya Yamanaka
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Abstract

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 {\it c}-number by hand, for satisfying the Goldstone theorem. Furthermore, we confirm that the unitary inequivalence of vacua in the spontaneous symmetry breakdown is true for the finite volume system.

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Hiroaki Enomoto, Masahiko Okumura, Yoshiya Yamanaka. 2006-02-08. Goldstone Theorem, Hugenholtz-Pines Theorem and Ward-Takahashi Relation in Finite Volume Bose-Einstein Condensed Gases. https://doi.org/10.1016/j.aop.2005.12.009

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