TY - JOUR

T1 - Ward-Takahashi relation at finite temperature in Bose-Einstein condensation of trapped neutral atoms

AU - Okumura, Masahiko

AU - Yamanaka, Yoshiya

N1 - Funding Information:
The authors would like to thank Professors I. Ohba and H. Nakazato for helpful comments and encouragements, and Dr. M. Mine for useful discussions. The authors also thank the Yukawa Institute for Theoretical Physics at Kyoto University, where this work was initiated during the YITP-W-03-10 on “Thermal Quantum Field Theories and Their Applications”. One of the authors (M.O.) is supported partially by the Grant-in-Aid for The 21st Century COE Program (Physics of Self-Organization Systems) at Waseda University and that for Priority Area B (#763), MEXT. One of the authors (Y.Y.) wishes to express his thanks for (i) Grant-in-Aid for Scientific Research and Open Research Center Project, MEXT, and (ii) Waseda University Grant for Special Research Projects (2004A-186).

PY - 2005/3/15

Y1 - 2005/3/15

N2 - 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.

AB - 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.

KW - Bose-Einstein condensation

KW - Thermo field dynamics

KW - Ward-Takahashi relation

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U2 - 10.1016/j.physa.2004.10.006

DO - 10.1016/j.physa.2004.10.006

M3 - Article

AN - SCOPUS:11444261182

VL - 348

SP - 157

EP - 172

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -