Explicit Proof of Equivalence of Two—Point Functions in the Two Formalisms of Thermal Field Theory
Explicit Proof of Equivalence of Two-Point Functions in the Two Formalisms of Thermal Field Theory
摘要
We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal theory based on the expressions in the real-time formalism and indicate that the key point of completing the proof is to separate carefully the imaginary part of the zero-temperature loop integral from relevant expressions and this fact will certainly be very useful for examination of the equivalent problem of two formalisms of thermal field theory in other theories, including the one of the propagators for scalar bound states in an NJL model.
基金
国家自然科学基金
参考文献12
-
1D.A. Kirzhnits and A.D. Linde, Phys. Lett. B42 (1972)471; S. Weinberg, Phys. Rev. D7 (1973) 2887; D9 (1974)3357; L. Dolan and R. Jackiw, ibid. D9 (1974) 3320.
-
2A.D. Linde, Rep. Prog. Phys. 42 (1979) 389; L. Girardello, M.T. Grisaru and P. Salomonson, Nucl. Phys.B178 (1981) 331; B. de Witt, Fundamental Interactions,Cargese (1981), eds M. Levy, et al., Plenum, New York (1982); R.H. Brandenberger, Rev. Mod. Phys. 57 (1985)1.
-
3H. Umezawa, H. Matsumoto and M. Tachiki, ThermoField Dynamics and Condensed Matter States, NorthHolland, Amsterdam (1982); K.C. CHOU, Z.B. SU, B.L.HAO and L. YU, Phys. Rep. 118 (1985) 1.
-
4N.P. Landsman and Ch.G. van Weert, Phys. Rep. 145(1987) 141.
-
5J.I. Kapusta, Finite-Temperature Field Theory, Cambridge University Press, Cambridge, England (1989).
-
6Y. Fujimoto, R. Grigjanis and H. Nishino, Phys. Lett.B141 (1984) 83; Y. Fujimoto and R. Grigjanis, Z. Phys.C28 (1985) 395; Prog. Theor. Phys. 74 (1985) 1105; R..Kobes, Phys. Rev. D42 (1990) 562; D43 (1991) 1269; E.Braaten and R. Pisarski, Phys. Rev. Lett. 64 (1990) 1338;Nucl. Phys. B337 (1990) 569; J. Frenkel and J.C. Taylor,Nucl. Phys. B334 (1990) 199; R. Kobes, Phys. Rev. Lett.67 (1991) 1384.
-
7B.R. ZHOU, Phys. Rev. D62 (2000) 105004.
-
8Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961)345; 124 (1961) 246.
-
9T.S. Evans, Phys. Lett. B249 (1990) 286; B252 (1990)108.
-
10R.L. Kobes and G.W. Semenoff, Nucl. Phys. B260 (1985)714; ibid. B272 (1986) 329.
-
1ZHOUBang-Rong.Two—Point Function Reduction of Four—Point Amputated Functions and Transformations in FF and RA Basis in a Real—Time Finite Temperature NJL Model[J].Communications in Theoretical Physics,2002,37(6):685-692.
-
2漆书家.谈谈各种积分的内在联系和统一记号[J].华东交通大学学报,1993,10(1):104-110.
-
3王金芝.二重极限[J].科技致富向导,2010,0(10Z):134-135.
-
4Wang, YM,Guo, BY.ON NUMEROV SCHEME FOR NONLINEAR TWO-POINTS BOUNDARY VALUE PROBLEM[J].Journal of Computational Mathematics,1998,16(4):345-351. 被引量:9
-
5王信峰,葛玉安,曾庆黎.Solutions of Two-point BVP in Banach Spaces[J].Tsinghua Science and Technology,1998,3(4):1265-1269.
-
6石玉峰.SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS[J].Acta Mathematicae Applicatae Sinica,1999,15(4):409-417.
-
7Yao Qingliu.POSITIVE SOLUTIONS TO A SEMILINEAR SYSTEM OF SECOND-ORDER TWO-POINT BOUNDARY VALUE PROBLEMS[J].Annals of Differential Equations,2006,22(1):87-94. 被引量:1
-
8黄春潮.POSITIVE SOLUTIONS OF TWO-POINT BOUNDARY VALUE PROBLEMS OF DIFFERENTIO-INTEGRAL EQUATIONS[J].Annals of Differential Equations,1998,14(2):78-86.
-
9Feng Yuqiang,Liu Sanyang.ON THE EXISTENCE,MULTIPLICITY AND UNIQUENESS OF POSITIVE SOLUTION FOR A THIRD ORDER TWO-POINT BOUNDARY VALUE PROBLEM[J].Annals of Differential Equations,2005,21(3):271-274. 被引量:2
-
10张建华.例析以双曲线为载体的多边形的中考题[J].数学大世界(初中版),2015,0(7):70-73.