Stability of the Classical Solutions of Gauge Theory

YIN Yu-Dong; HUANG Tao

Chinese Physics C> 2002, Vol. 26> Issue(1) : 28-34

Stability of the Classical Solutions of Gauge Theory

YIN Yu-Dong ^, ,
HUANG Tao

Department of Physics, Capital Normal University, Beijing 100037, China2 Institute of High Energy Physics, The Chinese Academy of Sciences, Beijing 100039, China

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We introduce the lagrange multiplier method to study the stability of a classical solution. We analyze the Hessian form of a starting point in the O(3) sigma model and generalize the result to the gauge theory. We conclude that the stability of a classicalsolution of the gauge theory is determined by the second variation of the effective Lagrangian including the contribution of the lagrange multiplier. The variational sign of the classical energy functional is a judgement of the solution stability.

References

[1]

. Klinkhamer F R. Phys. Lett., 1990, B246: 1312. Arnold P, Mclerran L. Phys. Rev., 1987, D36: 5813. Kunz J, Brihaye Y. Phys. Lett., 1989, B216: 3534. Kuzimin V. Rubakov V, Shaposhinikov M. Phys. Lett., 1985, B155: 365. Vachaspati T. Phys. Rev. Lett., 1992, 68: 1977; 1992, 69: 2166. Nielsen H B, Olesen P., Nucl. Phys., 1973, B61: 45 7. Vachaspati T, Barriola M. Phys. Rev. Lett., 1992, 69: 868. Barriola M, Vachaspati T. Phys. Rev., 1994, D50: 28199. Manton N S. Phys. Rev., 1983, D28: 2019 10. Mottola E, Wipf A. Phys. Rev., 1989, D39: 588; Mccleran L. ACTA Physica Polonica, 1989, B28: 24911. Klinkhamer F R, Olesen P. Nucl. Phys., 1994, B422: 22712. Yaffe L G. Phys. Rev., 1989, D40: 346313. James M. Perivolaropoulos L, Vachaspati T. Phys. Rev., 1992, D46: 5232; Nucl. Phys., 1993, B359: 534 14. Klinkhame F R, Monton S N. Phys. Rev., 1984, D30: 2212 15. Brihaye Y, Kosinski P. Mod. Phys. Lett., 1999, A4: 24716. Goodband M, Hindmarsh M. Phys. Rev., 1995, D52: 4621; Phys. Lett., 1995, B363: 5817. Gustafson S, Sigal I M. Comm. Math. Phys., 2000, 210: 25718. Brihaye Y, Giller S, Kosinski P et al. Phys. Lett., 1992, B293: 383; Bochkarev A I. Shaposhnikov M E. Mod. Phys. Lett., 1987, A2: 99119. Abdalla E. 2 Dimensional Quantum Field Theory, World Scientific, 199120. YIN Yu-Dong, WEN Jia-Ru, HUANG Tao. Phys. Lett., 1996, B373: 30921. YIN Yu-Dong, HUANG Tao. The Stability of Static Solutions under Parametrizations in the O(3) σ Model in 1+1 Dimension, preprint

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YIN Yu-Dong and HUANG Tao. Stability of the Classical Solutions of Gauge Theory[J]. Chinese Physics C, 2002, 26(1): 28-34.

YIN Yu-Dong and HUANG Tao. Stability of the Classical Solutions of Gauge Theory[J]. Chinese Physics C, 2002, 26(1): 28-34. shu

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Received: 2001-05-08
Revised: 1900-01-01

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通讯作者: 陈斌, [email protected]

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沈阳化工大学材料科学与工程学院沈阳 110142

Stability of the Classical Solutions of Gauge Theory

Corresponding author: YIN Yu-Dong,

Department of Physics, Capital Normal University, Beijing 100037, China2 Institute of High Energy Physics, The Chinese Academy of Sciences, Beijing 100039, China

Received Date: 2001-05-08

Accepted Date: 1900-01-01

Available Online: 2002-01-05

Abstract: We introduce the lagrange multiplier method to study the stability of a classical solution. We analyze the Hessian form of a starting point in the O(3) sigma model and generalize the result to the gauge theory. We conclude that the stability of a classicalsolution of the gauge theory is determined by the second variation of the effective Lagrangian including the contribution of the lagrange multiplier. The variational sign of the classical energy functional is a judgement of the solution stability.

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Stability of the Classical Solutions of Gauge Theory

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