Applicability of the linear δ expansion for the λ 4 field theory at finite temperature in the symmetric and broken phases

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 78, Issue 6, 2008, Pages

  Farias, R L S ^a   Krein, G ^b   Ramos, Rudnei O ^a  

^a STATE UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 53549110504     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.78.065046     Document Type: Article

References (107)

1. M. Le Bellac, Thermal Field Theory (Cambridge University Press, Cambridge, England, 1996).
2. M. Gleiser and R.O. Ramos, Phys. Lett. B 300, 271 (1993). PYLBAJ 0370-2693 10.1016/0370-2693(93)90365-O
3. J.-P. Blaizot, E. Iancu, and A.K. Rebhan, AIP Conf. Proc. 739, 63 (2004). APCPCS 0094-243X 10.1063/1.1843592
4. D.H. Rischke, Prog. Part. Nucl. Phys. 52, 197 (2004). PPNPDB 0146-6410 10.1016/j.ppnp.2003.09.002
5. U. Kraemmer and A.K. Rebhan, Rep. Prog. Phys. RPPHAG 0034-4885 67, 351 (2004). 10.1088/0034-4885/67/3/R05
6. J.O. Andersen and M. Strickland, Ann. Phys. (N.Y.) APNYA6 0003-4916 317, 281 (2005).
7. J.R. Espinosa, M. Quirós, and F. Zwirner, Phys. Lett. B 291, 115 (1992). PYLBAJ 0370-2693 10.1016/0370-2693(92)90129-R
8. J. Arafune, K. Ogata, and J. Sato, Prog. Theor. Phys. 99, 119 (1998). PTPKAV 0033-068X 10.1143/PTP.99.119
9. G. Amelino-Camelia and S.-Y. Pi, Phys. Rev. D 47, 2356 (1993). PRVDAQ 0556-2821 10.1103/PhysRevD.47.2356
10. N. Banerjee and S. Mallik, Phys. Rev. D 43, 3368 (1991). PRVDAQ 0556-2821 10.1103/PhysRevD.43.3368
11. R.R. Parwani, Phys. Rev. D 45, 4695 (1992); PRVDAQ 0556-2821 10.1103/PhysRevD.45.4695
12. R.R. Parwani Phys. Rev. D 48, 5965(E) (1993). PRVDAQ 0556-2821 10.1103/PhysRevD.48.5965.2
13. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University, New York, 1996).
14. S. Muroya, A. Nakamura, C. Nonaka, and T. Takaishi, Prog. Theor. Phys. 110, 615 (2003). PTPKAV 0033-068X 10.1143/PTP.110.615
15. M.E. Carrington, Phys. Rev. D 45, 2933 (1992). PRVDAQ 0556-2821 10.1103/PhysRevD.45.2933
16. P. Arnold and O. Espinosa, Phys. Rev. D 47, 3546 (1993). PRVDAQ 0556-2821 10.1103/PhysRevD.47.3546
17. B. Gruter, R. Alkofer, A. Maas, and J. Wambach, Eur. Phys. J. C 42, 109 (2005). EPCFFB 1434-6044 10.1140/epjc/s2005-02282-1
18. E. Braaten and R.D. Pisarski, Nucl. Phys. NUPBBO 0550-3213 B337, 569 (1990); 10.1016/0550-3213(90)90508-B
19. J. Frenkel and J.C. Taylor, Nucl. Phys. NUPBBO 0550-3213 B334, 199 (1990); 10.1016/0550-3213(90)90661-V
20. J.C. Taylor and S.M.H. Wong, Nucl. Phys. NUPBBO 0550-3213 B346, 115 (1990). 10.1016/0550-3213(90)90240-E
21. J.O. Andersen, E. Braaten, and M. Strickland, Phys. Rev. Lett. 83, 2139 (1999); PRLTAO 0031-9007 10.1103/PhysRevLett.83.2139
22. J.O. Andersen E. Braaten M. Strickland Phys. Rev. D 61, 014017 (1999); PRVDAQ 0556-2821 10.1103/PhysRevD.61.014017
23. J.O. Andersen E. Braaten M. Strickland Phys. Rev. D 61, 074016 (2000); PRVDAQ 0556-2821 10.1103/PhysRevD.61.074016
24. J.O. Andersen, E. Braaten, E. Petitgirard, and M. Strickland, Phys. Rev. D 66, 085016 (2002); PRVDAQ 0556-2821 10.1103/PhysRevD.66.085016
25. J.O. Andersen, E. Petitgirard, and M. Strickland, Phys. Rev. D 70, 045001 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.70.045001
26. F. Karsch, A. Patkós, and P. Petreczky, Phys. Lett. B 401, 69 (1997); PYLBAJ 0370-2693 10.1016/S0370-2693(97)00392-4
27. J.O. Andersen and M. Strickland, Phys. Rev. D 64, 105012 (2001); PRVDAQ 0556-2821 10.1103/PhysRevD.64.105012
28. J.O. Andersen M. Strickland Phys. Rev. D 71, 025011 (2005); PRVDAQ 0556-2821 10.1103/PhysRevD.71.025011
29. J.O. Andersen and L. Kyllingstad, arXiv:hep-ph/0805.4478.
30. J.O. Andersen, E. Braaten, and M. Strickland, Phys. Rev. D 63, 105008 (2001). PRVDAQ 0556-2821 10.1103/PhysRevD.63.105008
31. J.M. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D 10, 2428 (1974). PRVDAQ 0556-2821 10.1103/PhysRevD.10.2428
32. J. Berges, Sz. Borsanyi, U. Reinosa, and J. Serreau, Phys. Rev. D 71, 105004 (2005). PRVDAQ 0556-2821 10.1103/PhysRevD.71.105004
33. J.-P. Blaizot, E. Iancu, and A. Rebhan, Phys. Lett. B 470, 181 (1999). PYLBAJ 0370-2693 10.1016/S0370-2693(99)01306-4
34. J.-P. Blaizot, E. Iancu, and A. Rebhan, Phys. Rev. Lett. 83, 2906 (1999). PRLTAO 0031-9007 10.1103/PhysRevLett.83.2906
35. J.-P. Blaizot, E. Iancu, and A. Rebhan, Phys. Rev. D 63, 065003 (2001). PRVDAQ 0556-2821 10.1103/PhysRevD.63.065003
36. A. Peshier, Phys. Rev. D 63, 105004 (2001). PRVDAQ 0556-2821 10.1103/PhysRevD.63.105004
37. H. Van Hees and J. Knoll, Phys. Rev. D 65, 025010 (2001); PRVDAQ 0556-2821 10.1103/PhysRevD.65.025010
38. H. Van Hees J. Knoll Phys. Rev. D 65, 105005 (2002); PRVDAQ 0556-2821 10.1103/PhysRevD.65.105005
39. J.-P. Blaizot, E. Iancu, and U. Reinosa, Phys. Lett. B 568, 160 (2003); PYLBAJ 0370-2693 10.1016/j.physletb.2003.06.008
40. J.-P. Blaizot E. Iancu U. Reinosa Nucl. Phys. A 736, 149 (2004); NUPABL 0375-9474 10.1016/j.nuclphysa.2004.02.019
41. J. Berges, S. Borsanyi, U. Reinosa, and J. Serreau, Ann. Phys. (N.Y.) APNYA6 0003-4916 320, 344 (2005); 10.1016/j.aop.2005.06.001
42. G. Fejos, A. Patkos, and Zs. Szep, Nucl. Phys. A803, 115 (2008); NUPABL 0375-9474
43. A. Arrizabalaga and U. Reinosa, Nucl. Phys. A785, 234 (2007); NUPABL 0375-9474 10.1016/j.nuclphysa.2006.11.143
44. A. Arrizabalaga U. Reinosa Eur. Phys. J. A 31, 754 (2007). EPJAFV 1434-6001 10.1140/epja/i2007-10008-4
45. E. Braaten and E. Petitgirard, Phys. Rev. D 65, 085039 (2002). PRVDAQ 0556-2821 10.1103/PhysRevD.65.085039
46. A. Okopinska, Phys. Rev. D 35, 1835 (1987); PRVDAQ 0556-2821 10.1103/PhysRevD.35.1835
47. M. Moshe and A. Duncan, Phys. Lett. B 215, 352 (1988). PYLBAJ 0370-2693 10.1016/0370-2693(88)91447-5
48. J.-L. Kneur, M.B. Pinto, and R.O. Ramos, Phys. Rev. D 74, 125020 (2006); PRVDAQ 0556-2821 10.1103/PhysRevD.74.125020
49. J.-L. Kneur M.B. Pinto R.O. Ramos Braz. J. Phys. 37, 258 (2007); BJPHE6 0103-9733 10.1590/S0103-97332007000200016
50. J.-L. Kneur M.B. Pinto R.O. Ramos Int. J. Mod. Phys. E 16, 2798 (2007); IMPEER 0218-3013 10.1142/S0218301307008434
51. J.-L. Kneur, M.B. Pinto, R.O. Ramos, and E. Staudt, Phys. Rev. D 76, 045020 (2007); PRVDAQ 0556-2821 10.1103/PhysRevD.76.045020
52. J.-L. Kneur M.B. Pinto R.O. Ramos E. Staudt Phys. Lett. B 657, 136 (2007); PYLBAJ 0370-2693
53. J.-L. Kneur M.B. Pinto R.O. Ramos E. Staudt Int. J. Mod. Phys. E 16, 2802 (2007). IMPEER 0218-3013 10.1142/S0218301307008446
54. M.B. Pinto and R.O. Ramos, Phys. Rev. D 60, 105005 (1999). PRVDAQ 0556-2821 10.1103/PhysRevD.60.105005
55. M.B. Pinto and R.O. Ramos, Phys. Rev. D 61, 125016 (2000). PRVDAQ 0556-2821 10.1103/PhysRevD.61.125016
56. V.I. Yukalov, Moscow Univ. Phys. Bull. MUPBAC 0027-1349 31, 10 (1976);
57. V.I. Yukalov Theor. Math. Phys. TMPHAH 0040-5779 28, 652 (1976); 10.1007/BF01028917
58. R. Seznec and J. Zinn-Justin, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 20, 1398 (1979); 10.1063/1.524247
59. J.C. Le Guillou and J. Zinn-Justin, Ann. Phys. (N.Y.) APNYA6 0003-4916 147, 57 (1983); 10.1016/0003-4916(83)90067-2
60. W.E. Caswell, Ann. Phys. (N.Y.) APNYA6 0003-4916 123, 153 (1979); 10.1016/0003-4916(79)90269-0
61. I.G. Halliday and P. Suranyi, Phys. Lett. B 85, 421 (1979); PYLBAJ 0370-2693 10.1016/0370-2693(79)91287-5
62. J. Killinbeck, J. Phys. A JPHAC5 0305-4470 14, 1005 (1981); 10.1088/0305-4470/14/5/020
63. R.P. Feynman and H. Kleinert, Phys. Rev. A 34, 5080 (1986); PLRAAN 1050-2947 10.1103/PhysRevA.34.5080
64. H.F. Jones and M. Moshe, Phys. Lett. B 234, 492 (1990); PYLBAJ 0370-2693 10.1016/0370-2693(90)92045-K
65. A. Neveu, Nucl. Phys. B, Proc. Suppl. NPBSE7 0920-5632 18, 242 (1991); 10.1016/0920-5632(91)90137-4
66. V. Yukalov, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 32, 1235 (1991); 10.1063/1.529320
67. C.M. Bender, K.A. Milton, and M. Moshe, Phys. Rev. D 45, 1248 (1992); PRVDAQ 0556-2821 10.1103/PhysRevD.45.1248
68. S. Gandhi and M.B. Pinto, Phys. Rev. D 46, 2570 (1992); PRVDAQ 0556-2821 10.1103/PhysRevD.46.2570
69. H. Yamada, Z. Phys. C 59, 67 (1993); ZPCFD2 0170-9739 10.1007/BF01555840
70. K.G. Klimenko, Z. Phys. C 60, 677 (1993); ZPCFD2 0170-9739 10.1007/BF01558396
71. A.N. Sissakian, I.L. Solovtsov, and O.P. Solovtsova, Phys. Lett. B 321, 381 (1994); PYLBAJ 0370-2693 10.1016/0370-2693(94)90262-3
72. H. Kleinert, Phys. Rev. D 57, 2264 (1998); PRVDAQ 0556-2821 10.1103/PhysRevD.57.2264
73. H. Kleinert Phys. Lett. B 434, 74 (1998); PYLBAJ 0370-2693 10.1016/S0370-2693(98)00750-3
74. for a review, see H. Kleinert and V. Schulte-Frohlinde, Critical Properties of 4-Theories (World Scientific, Singapore, 2001), Chap.;
75. M.B. Pinto, R.O. Ramos, and P.J. Sena, Physica A (Amsterdam) 342, 570 (2004). PHYADX 0378-4371 10.1016/j.physa.2004.05.042
76. G. Krein, D.P. Menezes, and M.B. Pinto, Phys. Lett. B 370, 5 (1996); PYLBAJ 0370-2693 10.1016/0370-2693(95)01578-7
77. G. Krein, R.S.M. de Carvalho, D.P. Menezes, M. Nielsen, and M.B. Pinto, Eur. Phys. J. A 1, 45 (1998); EPJAFV 1434-6001 10.1007/s100500050030
78. G. Krein, D.P. Menezes, and M.B. Pinto, Braz. J. Phys. 28, 66 (1998). BJPHE6 0103-9733 10.1590/S0103-97331998000100009
79. P.M. Stevenson, Phys. Rev. D 23, 2916 (1981); PRVDAQ 0556-2821 10.1103/PhysRevD.23.2916
80. For other optimization schemes, please see: V.I. Yukalov and E.P. Yukalova, Ann. Phys. (N.Y.) APNYA6 0003-4916 277, 219 (1999); 10.1006/aphy.1999.5953
81. V.I. Yukalov and E.P. Yukalova, Chaos Solitons Fractals CSFOEH 0960-0779 14, 839 (2002). 10.1016/S0960-0779(02)00029-2
82. M.C.B. Abdalla, J.A. Helayel-Neto, Daniel L. Nedel, and Carlos R. Senise, Jr., Phys. Rev. D 77, 125020 (2008). PRVDAQ 0556-2821 10.1103/PhysRevD.77. 125020
83. I.R.C. Buckley, A. Duncan, and H.F. Jones, Phys. Rev. D 47, 2554 (1993); PRVDAQ 0556-2821 10.1103/PhysRevD.47.2554
84. C.M. Bender, A. Duncan, and H.F. Jones, Phys. Rev. D 49, 4219 (1994); PRVDAQ 0556-2821 10.1103/PhysRevD.49.4219
85. C. Arvanitis, H.F. Jones, and C.S. Parker, Phys. Rev. D 52, 3704 (1995); PRVDAQ 0556-2821 10.1103/PhysRevD.52.3704
86. H. Kleinert and W. Janke, Phys. Lett. A 206, 283 (1995); PYLAAG 0375-9601 10.1016/0375-9601(95)00521-4
87. R. Guida, K. Konishi, and H. Suzuki, Ann. Phys. (N.Y.) 241, 152 (1995); APNYA6 0003-4916 10.1006/aphy.1995.1059
88. R. Guida K. Konishi H. Suzuki Ann. Phys. (N.Y.) 249, 109 (1996); APNYA6 0003-4916 10.1006/aphy.1996.0066
89. B. Bellet, P. Garcia, and A. Neveu, Int. J. Mod. Phys. A IMPAEF 0217-751X 11, 5587 (1996); 10.1142/S0217751X9600256X
90. B. Bellet P. Garcia A. Neveu Int. J. Mod. Phys. A IMPAEF 0217-751X 11, 5607 (1996). 10.1142/S0217751X96002571
91. A. Duncan and H.F. Jones, Phys. Rev. D 47, 2560 (1993). PRVDAQ 0556-2821 10.1103/PhysRevD.47.2560
92. J.-L. Kneur and D. Reynaud, Eur. Phys. J. C 24, 323 (2002); EPCFFB 1434-6044 10.1007/s100520200951
93. J.-L. Kneur D. Reynaud Phys. Rev. D 66, 085020 (2002). PRVDAQ 0556-2821 10.1103/PhysRevD.66.085020
94. J.-L. Kneur, M.B. Pinto, and R.O. Ramos, Phys. Rev. Lett. 89, 210403 (2002); PRLTAO 0031-9007 10.1103/PhysRevLett.89.210403
95. J.-L. Kneur M.B. Pinto R.O. Ramos Phys. Rev. A 68, 043615 (2003); PLRAAN 1050-2947 10.1103/PhysRevA.68.043615
96. E. Braaten and E. Radescu, Phys. Rev. Lett. 89, 271602 (2002); PRLTAO 0031-9007 10.1103/PhysRevLett.89.271602
97. E. Braaten E. Radescu Phys. Rev. A 66, 063601 (2002). PLRAAN 1050-2947 10.1103/PhysRevA.66.063601
98. S. Chiku and T. Hatsuda, Phys. Rev. D 58, 076001 (1998). PRVDAQ 0556-2821 10.1103/PhysRevD.58.076001
99. L. Dolan and R. Jackiw, Phys. Rev. D 9, 3320 (1974); PRVDAQ 0556-2821 10.1103/PhysRevD.9.3320
100. S. Weinberg, Phys. Rev. D 9, 3357 (1974); PRVDAQ 0556-2821 10.1103/PhysRevD.9.3357
101. A. Linde, Rep. Prog. Phys. 42, 389 (1979). RPPHAG 0034-4885 10.1088/0034-4885/42/3/001
102. B.W. Lee, Nucl. Phys. NUPBBO 0550-3213 B9, 649 (1969); 10.1016/0550-3213(69)90065-0
103. B.W. Lee Chiral Dynamics (Gordon and Breach, New York, 1972).
104. T. Kugo, Prog. Theor. Phys. 57, 593 (1977). PTPKAV 0033-068X 10.1143/PTP.57.593
105. J.O. Andersen, E. Braaten, and M. Strickland, Phys. Rev. D 62, 045004 (2000). PRVDAQ 0556-2821 10.1103/PhysRevD.62.045004
106. F.G. Gardim and F.M. Steffens, Nucl. Phys. A 797, 50 (2007). NUPABL 0375-9474 10.1016/j.nuclphysa.2007.09.006
107. F.G. Gardim (private communication).