TY - JOUR

T1 - Goldstone theorem, Hugenholtz-Pines theorem, and Ward-Takahashi relation in finite volume Bose-Einstein condensed gases

AU - Enomoto, Hiroaki

AU - Okumura, Masahiko

AU - Yamanaka, Yoshiya

N1 - Funding Information:
The authors thank Professor I. Ohba and Professor H. Nakazato for helpful comments and encouragements, and Dr. M. Mine for useful discussions. The authors thank the Yukawa Institute for Theoretical Physics at Kyoto University for offering us the opportunity of discussions during the YITP workshop YITP-W-05-09 on “Thermal Quantum Field Theories and Their Applications,” useful to complete this work. This work is partly supported by a Grant-in-Aid for Scientific Research (C) (No. 17540364) from the Japan Society for the Promotion of Science, for Young Scientists (B) (No. 17740258) and for Priority Area Research (B) (No. 13135221) both from the Ministry of Education, Culture, Sports, Science and Technology, Japan. M.O. and Y.Y. express their thanks for Waseda University Grant for Special Research Projects (2005).

PY - 2006/8

Y1 - 2006/8

N2 - 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.

AB - 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.

KW - Bose-Einstein condensation

KW - Goldstone theorem

KW - Hugenholtz-Pines theorem

KW - Spontaneous symmetry breakdown

KW - Unitarily inequivalent vacua

KW - Ward-Takahashi relations

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U2 - 10.1016/j.aop.2005.12.009

DO - 10.1016/j.aop.2005.12.009

M3 - Article

AN - SCOPUS:33745501681

SN - 0003-4916

VL - 321

SP - 1892

EP - 1917

JO - Annals of Physics

JF - Annals of Physics

IS - 8

ER -