Thermal Soliton Correlation Functions in Theories with a Z(N) Symmetry

DOI: 10.4236/jmp.2012.311221   PDF   HTML   XML   4,049 Downloads   5,672 Views   Citations


We show that the quantum solitons occurring in theories describing a complex scalar field in (1 + 1)-dimensions with a Z(N) symmetry may be identified with sine-Gordon quantum solitons in the phase of this field. Then using both the Euclidean thermal Green function of the two-dimensional free massless scalar field in coordinate space and its dual, we obtain an explicit series expression for the corresponding solitonic correlation function at finite temperature.

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L. Mondaini, "Thermal Soliton Correlation Functions in Theories with a Z(N) Symmetry," Journal of Modern Physics, Vol. 3 No. 11, 2012, pp. 1776-1780. doi: 10.4236/jmp.2012.311221.

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The authors declare no conflicts of interest.


[1] L. Mondaini and E. C. Marino, “Sine-Gordon/Coulomb Gas Soliton Correlation Functions and an Exact Evaluation of the Kosterlitz-Thouless Critical Exponent,” Journal of Statistical Physics, Vol. 118, No. 3-4, 2005, pp. 767-779. doi:10.1007/s10955-004-8828-y
[2] S. Samuel, “Grand Partition Function in Field Theory with Applications to Sine-Gordon Field Theory,” Physical Review D, Vol. 18, No. 6, 1978, pp. 1916-1932. doi:10.1103/PhysRevD.18.1916
[3] J. M. Kosterlitz, “The Critical Properties of the Two-Dimensional XY Model,” Journal of Physics C: Solid State Physics, Vol. 7, No. 6, 1974, pp. 1046-1060. doi:10.1088/0022-3719/7/6/005
[4] A. B. Zamolodchikov and Al. B. Zamolodchikov, “Factorized S-Matrices in Two Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Theory Models,” Annals of Physics, Vol. 120, No. 2, 1979, pp. 253-291. doi:10.1016/0003-4916(79)90391-9
[5] V. E. Korepin, “The Mass Spectrum and the S Matrix of the Massive Thirring Model in the Repulsive Case,” Communications in Mathematical Physics, Vol. 76, No. 2, 1980, pp. 165-176. doi:10.1007/BF01212824
[6] L. Mondaini and E. C. Marino, “Dual Bosonic Thermal Green Function and Fermion Correlators of the Massive Thirring Model at Finite Temperature,” Modern Physics Letters A, Vol. 23, No. 10, 2008, pp. 761-767. doi:10.1142/S0217732308024390
[7] L. Mondaini, E. C. Marino and A. A. Schmidt, “Vanishing Conductivity of Quantum Solitons in Polyacetylene,” Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 5, 2009, p. 055401. doi:10.1088/1751-8113/42/5/055401
[8] E. C. Marino and J. A. Swieca, “Order, Disorder and Generalized Statistics,” Nuclear Physics B, Vol. 170, No. 1, 1980, pp. 175-186. doi:10.1016/0550-3213(80)90485-X
[9] E. C. Marino, B. Schroer and J. A. Swieca, “Euclidean Functional Integral Approach for Disorder Variables and Kinks,” Nuclear Physics B, Vol. 200, No. 3, 1982, pp. 473-497. doi:10.1016/0550-3213(82)90523-5
[10] E. C. Marino, “Dual Quantization of Solitons,” In: D. Baeriswyl, A. R. Bishop and J. Carmelo, Eds., Applications of Statistical and Field Theory Methods to Condensed Matter, Plenum Press, New York, 1990, pp. 121-140.
[11] L. Mondaini, “Obtaining a Closed-Form Representation for the Dual Bosonic Thermal Green Function by Using Methods of Integration on the Complex Plane,” Revista Brasileira de Ensino de Física, Vol. 34, No. 3, 2012, p. 3305.
[12] S. Mandelstam, “Soliton Operators for the Quantized Sine-Gordon Equation,” Physical Review D, Vol. 11, No. 10, 1975, pp. 3026-3030. doi:10.1103/PhysRevD.11.3026
[13] A. Gomez Nicola and D. A. Steer, “Thermal Bosonisation in the Sine-Gordon and Massive Thirring Models,” Nuclear Physics B, Vol. 549, No. 1-2, 1999, pp. 409-449. doi:10.1016/S0550-3213(99)00128-5
[14] A. Das, “Finite Temperature Field Theory,” World Scientific, Singapore, 1997.
[15] D. Delepine, R. Gonzalez Felipe and J. Weyers, “Equivalence of the Sine-Gordon and Massive Thirring Models at Finite Temperature,” Physics Letters B, Vol. 419, No. 1-4, 1998, pp. 296-302. doi:10.1016/S0370-2693(97)01436-6
[16] S. Coleman, “Quantum Sine-Gordon Equation as the Massive Thirring Model,” Physical Review D, Vol. 11, No. 8, 1975, pp. 2088-2097. doi:10.1103/PhysRevD.11.2088

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