Relation between generalized Bogoliubov and Bogoliubov-de Gennes approaches including Nambu-Goldstone mode

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Abstract

The two approaches of consistent quantum field theory for systems of the trapped Bose-Einstein condensates are known, one is the Bogoliubov-de Gennes approach and the other is the generalized Bogoliubov approach. In this paper, we investigate the relation between the two approaches and show that they are formally equivalent to each other. To do this one must carefully treat the Nambu-Goldstone mode which plays a crucial role in the condensation. It is emphasized that the choice of vacuum is physically relevant.

Original languageEnglish
Article number042307
JournalJournal of Mathematical Physics
Volume46
Issue number4
DOIs
Publication statusPublished - 2005 Apr

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Bose-Einstein Condensate
Quantum Field Theory
Condensation
Bose-Einstein condensates
Vacuum
condensation
vacuum

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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abstract = "The two approaches of consistent quantum field theory for systems of the trapped Bose-Einstein condensates are known, one is the Bogoliubov-de Gennes approach and the other is the generalized Bogoliubov approach. In this paper, we investigate the relation between the two approaches and show that they are formally equivalent to each other. To do this one must carefully treat the Nambu-Goldstone mode which plays a crucial role in the condensation. It is emphasized that the choice of vacuum is physically relevant.",
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AB - The two approaches of consistent quantum field theory for systems of the trapped Bose-Einstein condensates are known, one is the Bogoliubov-de Gennes approach and the other is the generalized Bogoliubov approach. In this paper, we investigate the relation between the two approaches and show that they are formally equivalent to each other. To do this one must carefully treat the Nambu-Goldstone mode which plays a crucial role in the condensation. It is emphasized that the choice of vacuum is physically relevant.

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