### 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 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 language | English |
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Pages (from-to) | 1892-1917 |

Number of pages | 26 |

Journal | Annals of Physics |

Volume | 321 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2006 Aug 1 |

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### Keywords

- 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)

### Cite this

*Annals of Physics*,

*321*(8), 1892-1917. https://doi.org/10.1016/j.aop.2005.12.009