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

Abstract
HTML
Reference
Related

PDF

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.

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

[1]	WANG Xiao , CAO Yun , CHEN Liang , DU Han-Wen , YIN Li-Xin . Mechanical Stability Analysis of BPM Support at SSRF. Chinese Physics C, 2008, 32(S1): 28-30.
[2]	YANG Yu-Feng , ZHU Xiong-Wei . Microbunch Instability in Wigglers. Chinese Physics C, 2007, 31(8): 778-782.
[3]	Alexander W.Chao . Gravitational Instability of a Nonrotating Galaxy. Chinese Physics C, 2006, 30(S1): 6-10.
[4]	GUO Zhi-Yuan , LIU Yu-Dong , Qin Qing , WANG Jiu-Qing , XING Jun . The Studies of Electron Cloud Instability in the BEPC. Chinese Physics C, 2006, 30(S1): 102-104.
[5]	LIU Yu-Dong , GUO Zhi-Yuan , QIN Qing , WANG Jiu-Qing . Electron Cloud Instability Simulation Studies for BEPCⅡ. Chinese Physics C, 2004, 28(11): 1222-1226.
[6]	YANG Jian-Cheng , XIA Jia-Wen , WU Jun-Xia , XIA Guo-Xing , LIU Wei , YIN Xue-Jun , LIU Yong , ZHOU Xue-Mei , MAO Li-Jun . Effect of Tune Modulation on the Transverse Stability of Storage Ring. Chinese Physics C, 2004, 28(11): 1203-1208.
[7]	ZHAO Zhen-Tang , JIANG Bo-Cheng . Longitudinal Coupled Bunch Instability in Fractionally Filled Storage Rings. Chinese Physics C, 2004, 28(11): 1209-1213.
[8]	OUYANG Hua-Fu , FU Shi-Nian , GUAN Xia-Ling , XU Wen-Wu . Study on the Design of an Intense-Beam RFQ with Stabilization. Chinese Physics C, 2004, 28(7): 753-757.
[9]	LIU Bo , LV Cai-Dian , GUO Hua , HE Ze-Jun . Mechanical and Chemical Instabilities in Nuclear Matter. Chinese Physics C, 2002, 26(10): 1056-1064.
[10]	XIONG Chun , HOU De-Fu . Medium Effects and Thermal Instability in φ₆³ Theory. Chinese Physics C, 2002, 26(8): 753-758.
[11]	WANG Shao-Shun , WU Chong . Erraticity of (Pseudo-)Rapidity Gaps. Chinese Physics C, 2001, 25(3): 183-187.
[12]	LUO Yun , ZHANG Chuang , GUO Zhi-Yuan . Study of Ion Induced Instability in BTCF. Chinese Physics C, 2001, 25(5): 437-442.
[13]	LUO Yun , GUO Zhi-Yuan , ZHANG Chuang . Analysis of an Ion Induced Coupled Bunch Instability in BEPC. Chinese Physics C, 2001, 25(3): 258-263.
[14]	LI YongJun , JIN YuMing , LI WeiMin , SUN BaoGen , YIN LiXin , LIU ZuPing , DIAO CaoZheng , LIU GongFa , ZHOU AnQi , LI JingYi , YU XiangKun , HE XiaoYe . Simulation of Ion-trapping Instability and Beam Shaking in an Electron Storage Ring. Chinese Physics C, 2000, 24(9): 864-869.
[15]	WANG LanFa , ZHANG Chuang , WANG ShuHong , GUO ZhiYuan . Study on Longitudinal Coupled Bunch Instability with Unequal Spaced Distribution. Chinese Physics C, 2000, 24(8): 761-766.
[16]	Wang Lanfa , Zhang Chuang , Wang Shuhong , Guo Zhiyuan , Lin Yuzheng , Tong Dechun . Simulation of Coupled Bunch Instability. Chinese Physics C, 1998, 22(12): 1174-1181.
[17]	WANG Shu-Hong . RESEARCH ON THE TRANSVERSE STABILITY OF THE CENTRAL BEAM IN A WAKE FIELD ACCELERATOR. Chinese Physics C, 1986, 10(6): 697-703.
[18]	YAN Tai-Xuan , SUN Li-Bo . THE TIME RESPONSE OF THE FERRITE LOADED CAVITY AND STABILITY OF BIAS AUTOTUNING SYSTEM. Chinese Physics C, 1983, 7(3): 346-354.
[19]	MA ZHONG-QI , DONG FANG-XIAO , ZHOU XIAN-JIAN , XUE PEI-YOU . CLASSICAL STATIC AND SPHERICALLY SYMMETRIC SOLUTION OF SU(3) GAUGE FIELD WITH A STATIC AND ECTERNAL EXTERNAL SOURCE. Chinese Physics C, 1981, 5(2): 182-191.
[20]	Dong Fang-xiao , Zhou Xian-jian , Huang Tao , Xue Pei-you . THE TIME-DEPENDENCES OF THE STATIC SOLUTION OF SU(2) AND SU(3) GAUGE THEORY AT THE PRESENCE OF STATIC EXTENDED SOURCE. Chinese Physics C, 1980, 4(6): 724-734.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(3117)
PDF Downloads(578)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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.

HTML

Reference (1)

Stability of the Classical Solutions of Gauge Theory

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article