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In this paper we study the theory of nonrelativistic weakly interacting Bose gas from the point of view of effective field theory. Firstly, the nonrenormalizability of the theory is briefly discussed. Then, starting from the effective Lagrangian, the lowest order contributions of Feynman diagrams are calculated for the parameters in the effective Lagrangian. These illustrate the running coupling constant phenomenon. After that, the differential align of the parameters in the effective Lagrangian is obtained. We show that the intrinsic energy scale of this effective theory can be removed, while it is not possible to do so for relativistic Bose gas. Our results can help to study the critical behavior of weakly interacting Bose gas.
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Keywords:
- Bose-Einstein condensation /
- quantum field theory /
- feynman diagram
[1] Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[2] Davis K B, Mewes M O, Andrews M R, van Druten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969
[3] Burnett K, Edwards M, Clark C W 1999 Phys. Today 52 37
[4] Leggett A J 2001 Rev. Mod. Phys. 73 307
[5] Andersen J O 2004 Rev. Mod. Phys. 76 599
[6] Boettcher I, Pawlowski J M, Diehl S 2012 Nucl. Phys. B 228 63
[7] Fisher M P, Weichman P B, Grinstein G, Fisher D S 1989 Phys. Rev. B 40 546
[8] Bloch I, Dalibard J, Zwerger W 2008 Rev. Mod. Phys. 80 885
[9] Haugset T, Haugerud H, Ravndal F 1998 Annals Phys. 266 27
[10] Braaten E, Nieto A 1999 Eur. Phys. J. B 11 143
[11] Braaten E, Hammer H W, Mehen T 2002 Phys. Rev. Lett. 88 040401
[12] Braaten E, Hammer H W, Hermans S 2001 Phys. Rev. A 63 063609
[13] Altland A 2010 Condensed Matter Field Theory. (London: Cambridge University Press) p251
[14] Tsvelik A 1996 Quantum Field Theory in Condensed Matter Physics (London: Cambridge University Press) p30
[15] Schakel A 2008 Boulevard of Broken Symmetries: Effective Field Theories of Condensed Matter (Singapore: World Scientific Press) p95
[16] Srednicki M 2007 Quantum Field Theory (London: Cambridge University Press) p129
[17] Maggiore M 2005 A Modern Introduction to Quantum Field Theory (London: Oxford University Press) p135
[18] Chen X W, Fang Z Y, Zhang J W, Zhong T, Tu W X 2011 Acta Phys. Sin. 60 021101 (in Chinese) [陈学文, 方祯云, 张家伟, 钟涛, 涂卫星 2011 60 021101]
[19] Polyanin A D, Manzhirov A V 2007 Handbook of Mathematics for Engineers and Scientists (Boca Raton FL: Chapman & Hall/CRC Press) p372
[20] Wilson K G 1971 Phys. Rev. B 4 3184
[21] Xu Y, Xiong Z Z, Li Z X, Chen B, Tan L 2009 Chin. Phys. B 18 4734
[22] Fan W, Xu Y, Chen B, Chen Z Y, Feng X L, Oh C H 2012 Phys. Rev. A 85 013645
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[1] Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[2] Davis K B, Mewes M O, Andrews M R, van Druten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969
[3] Burnett K, Edwards M, Clark C W 1999 Phys. Today 52 37
[4] Leggett A J 2001 Rev. Mod. Phys. 73 307
[5] Andersen J O 2004 Rev. Mod. Phys. 76 599
[6] Boettcher I, Pawlowski J M, Diehl S 2012 Nucl. Phys. B 228 63
[7] Fisher M P, Weichman P B, Grinstein G, Fisher D S 1989 Phys. Rev. B 40 546
[8] Bloch I, Dalibard J, Zwerger W 2008 Rev. Mod. Phys. 80 885
[9] Haugset T, Haugerud H, Ravndal F 1998 Annals Phys. 266 27
[10] Braaten E, Nieto A 1999 Eur. Phys. J. B 11 143
[11] Braaten E, Hammer H W, Mehen T 2002 Phys. Rev. Lett. 88 040401
[12] Braaten E, Hammer H W, Hermans S 2001 Phys. Rev. A 63 063609
[13] Altland A 2010 Condensed Matter Field Theory. (London: Cambridge University Press) p251
[14] Tsvelik A 1996 Quantum Field Theory in Condensed Matter Physics (London: Cambridge University Press) p30
[15] Schakel A 2008 Boulevard of Broken Symmetries: Effective Field Theories of Condensed Matter (Singapore: World Scientific Press) p95
[16] Srednicki M 2007 Quantum Field Theory (London: Cambridge University Press) p129
[17] Maggiore M 2005 A Modern Introduction to Quantum Field Theory (London: Oxford University Press) p135
[18] Chen X W, Fang Z Y, Zhang J W, Zhong T, Tu W X 2011 Acta Phys. Sin. 60 021101 (in Chinese) [陈学文, 方祯云, 张家伟, 钟涛, 涂卫星 2011 60 021101]
[19] Polyanin A D, Manzhirov A V 2007 Handbook of Mathematics for Engineers and Scientists (Boca Raton FL: Chapman & Hall/CRC Press) p372
[20] Wilson K G 1971 Phys. Rev. B 4 3184
[21] Xu Y, Xiong Z Z, Li Z X, Chen B, Tan L 2009 Chin. Phys. B 18 4734
[22] Fan W, Xu Y, Chen B, Chen Z Y, Feng X L, Oh C H 2012 Phys. Rev. A 85 013645
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