ON THE ANALYTICAL STUDY IN LATTICE GAUGE FIELD THEORY

CHEN De-Fang; SONG Yong-Shen; CHEN Tian-Lun; ZHENG Xi-Te; HE Xiang-Hao; XIAN Ding-Chang

Chinese Physics C> 1986, Vol. 10> Issue(1) : 32-39

ON THE ANALYTICAL STUDY IN LATTICE GAUGE FIELD THEORY

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Abstract：
The relation between the saddle point approximation and the action variational method in the lattice gauge field theory is discussed. It is expounded that in the thermodynamical limit by using a trial action composed of mean fields, the variational approach leads to the results as well as the higher order corrections obtained in the saddle point approximation. It is also pointed out that order by order corrections to the variational approach can be worked out systematically in an improved variational approach.

References

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K. Wilson, Phys. Rev, D10(1974), 2445.[2] Creutz, L. Jambs, and C. Rebbi, Phys. Reports, 95(1983), 201.[3] R. P. Feynman, and A. R. Hibbs "Quantum Mecanics and Path Integrals"; chap. 11, (NewYork, McGraw-Hill, 1965) .[4] J. M. Drouffe, Nucl. Phys, B170 [FSl](1980), 211; E. Brézín, and J. M. Drouffe, Nucl. Phys,B200[FS4](1982), 93.[5] J. M. Drouffe, and J. B. Zuber, Phys. Reports, 102(1983), 1.[6] K. Huang, "Statistical Mechanics", Chap. 9, (Cambridge, Massachusetts, 1963).[7] V. Alessandrini, V. Hakim, and A. Krzywicla, Nucl. Phys. B215 (FS7) (1983), I09; J. M. AIberty,H. FFyvbjerg, and B. Lautrup, Nucl. Phys, 8200 [FS8] (1983), 61.[8] Chen. T.-1, C. I. Tan; and Zheng X t., Phys. Lett, 109B(1982), 383; Zheng X.t, C. I. Tan and Chen T.1, Phys. Rev, D26(1982), 2843.[9] C.-T. Tan and Zheng X. t, Phys. Rev, D28 (1983), 3141.[10] S. H. Guo, Q. z. Chen, and J. m. Liu, Comm.Theor. Phys, (Beijing)6(1983), 346.[11] L. E. Reichl, "A Modern Course in Statistical Physics", Chap, 5, (University of Texas Press,Austin, 1980) .[12] X. T. Zheng, T. L. Chen and T. C. Hsien, Phys. Letts. 154B(1985), 166; X. H. He, Y. X.song and T. C. Hsien, Phys. Letts, 133B(1985), 417.

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CHEN De-Fang, SONG Yong-Shen, CHEN Tian-Lun, ZHENG Xi-Te, HE Xiang-Hao and XIAN Ding-Chang. ON THE ANALYTICAL STUDY IN LATTICE GAUGE FIELD THEORY[J]. Chinese Physics C, 1986, 10(1): 32-39.

CHEN De-Fang, SONG Yong-Shen, CHEN Tian-Lun, ZHENG Xi-Te, HE Xiang-Hao and XIAN Ding-Chang. ON THE ANALYTICAL STUDY IN LATTICE GAUGE FIELD THEORY[J]. Chinese Physics C, 1986, 10(1): 32-39. shu

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

ON THE ANALYTICAL STUDY IN LATTICE GAUGE FIELD THEORY

Corresponding author: CHEN De-Fang,

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1986-02-05

Abstract: The relation between the saddle point approximation and the action variational method in the lattice gauge field theory is discussed. It is expounded that in the thermodynamical limit by using a trial action composed of mean fields, the variational approach leads to the results as well as the higher order corrections obtained in the saddle point approximation. It is also pointed out that order by order corrections to the variational approach can be worked out systematically in an improved variational approach.