RIGHT TRANSLATION INVARIANT METRICS AND VARIATIONAL PRINCIPLES ON A PRINCIPAL BUNDLE——TREATED AS THE UNION OF SPACE-TIME AND AN INTERNAL SPACE

Wu Yong-shi; Lu Qi-keng

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1980, Vol. 4> Issue(3) : 322-336

RIGHT TRANSLATION INVARIANT METRICS AND VARIATIONAL PRINCIPLES ON A PRINCIPAL BUNDLE——TREATED AS THE UNION OF SPACE-TIME AND AN INTERNAL SPACE

Wu Yong-shi ,
Lu Qi-keng

Abstract
HTML
Reference
Related

PDF

Abstract：
In this paper, we discuss how to assign a metric on a principal bundle and howto rewrite the variational principles for a particle and for matter fields in an inva-riant from on the bundle in the principal-bundle formulation of gauge theories. Weshow that the right-translation invariant metric on the bundle must contain quantitieswhich transform exactly as gauge potentials, thus providing a new formalism for gaugefields. And we formulate the variational principle for a particle moving in the gaugefield as follows: The particle moves along a horizontal geodesic on the principalbundle. Starting from this we derive the Wong's equations of motion. Moreover, we elucidate the physical view-point which treats the bundle space asthe union of space-time and the internal space. Advantages of this viewpoint for un-derstanding the essentialities of gauge transformations and gauge invariance and forestablishing unified theories of gravitation and gauge fields are also discussed.

References

[1]

吴泳时、陈时、郭汉英,中国科学,1918年279页;Scientia Sinica, 21(1978),193.[2] R. Jackiw and C. Rebbi, Phys. Rev., D14(1976), 517.[3] 吴泳时、吴建时,科学通报,23(1978),601.[4] R .Jackiw and C. Rebbi. Phys. Rev. Lett., 36(1976), 1116.[5] 有关纤维丛的数学知识,可参阅陆启铿“纤维丛与规范场讲义”,(1973);或S. Kabayashi and B. Nomizu, "Foundations of Differential Geometry," Vol.1,1963.[6] Y. M. Cho, J. Math. Phys., 16(1975), 2029.[7] L. N. Chang, Ii. I.Macme and F. lsansouriy Pays. Rev., D13(1976), 235[8] 吴泳时、郭汉英,中国科学,1977年308页;Sctentia S4nica, 20(1977),186,[9] S. K. along. Nuovo Cvmento, 65A(1970), 689.[10] 陆启铿,物理学报,23(1974),249.[11] W. Greub, S. Halperin and R. Vanstein. "Connections, CurvatureCohomology", Vol.II,1973.[12] H. Whitney, ann. Math., 37(1935), 645.[13] C. N. Fang, Phys. rev. Lett., 33(1974), 445.[14] 郭汉英,科学通报,23(1978),407.[15] 吴泳时,Preprint IHES/P/79/271.,物理学报,29(1980),395.

[1]	QIU Jing , TANG Jing-Yu , WANG Sheng , WEI Jie . Studies of Transverse Phase Space Painting for the CSNS RCS Injection. Chinese Physics C, 2007, 31(10): 942-946.
[2]	WANG Jian-Hua , LI Kang . Split Angular Momentum in Noncommutative Phase Space. Chinese Physics C, 2006, 30(11): 1053-1057.
[3]	WANG Shao-Shun , WU Chong . Analysis of the Fluctuations in the Event-Space for NA27 Data. Chinese Physics C, 2002, 26(3): 216-221.
[4]	WANG Lan-Fa . Comments on Variational Method Used in Accelerating Structure. Chinese Physics C, 2002, 26(1): 74-78.
[5]	Chen Yinbao , Huang Zhibin . Nonlinear Space Charge Effects and Emittance Growth in Linac. Chinese Physics C, 1999, 23(12): 1231-1242.
[6]	Li Xiguo , Liu Hang , Liu Jianye . Two-Body Correlation Transport Theory for Heavy Ion Collisions Ⅱ.The Time-Evolution Equations of Single Particle States Given by Means of the Time Dependent Variational Principle and Antisymmetrized Molecular Dynamics. Chinese Physics C, 1997, 21(2): 162-168.
[7]	Lin Hai , Liu Lianshou . An Analytical Study of One-Dimensional Projection for the Self-Affine Fractal of Two-Dimensional Phase Space. Chinese Physics C, 1996, 20(7): 625-634.
[8]	Lin Hai , Zhang Yang , Liu Lianshou . An Analytic Study of Self-affine Fractal in Two-Dimensional Phase Space of High Energy Collisions. Chinese Physics C, 1996, 20(1): 65-75.
[9]	Wang Shaoshun , Xiao Chenguo , Zhang Jie , Xia Xiaojuan , Xiong Weijun , Zhong Yu . The Study of Particle Densities in Pseudorapidity Space in pp collisions at 400GeV/c. Chinese Physics C, 1994, 18(5): 392-397.
[10]	HUO Lei , JIANG Yu-Zhen , WANG Shan , ZHANG Wei-Ning , LIU Yi-Ming . Spatial Parameter from Two-pion Interferometry. Chinese Physics C, 1992, 16(9): 816-820.
[11]	CAI Rong-Gen , CHEN Zhi-Jian . The Boson Bound States in the Higher Dimensional Kerr Metric. Chinese Physics C, 1991, 15(5): 420-426.
[12]	SONG Zhong-Heng , WANG Xiao-Min . Calculation of Space Charge Field for Annulus and Disc Bunch of Charged Particles. Chinese Physics C, 1991, 15(1): 7-12.
[13]	LI Yuan-Jie . RADIAL SOLUTIONS OF THE DIRAC EQUATION IN A LEMAITRE METRIC. Chinese Physics C, 1989, 13(8): 701-705.
[14]	XU Kai-Wen . COVARIANT AND QUANTIZATION OF SPINNING STRING IN M_d×G SPACE-TIME. Chinese Physics C, 1988, 12(3): 315-323.
[15]	GAO Hong-Bo , SUN Yi . THE LOCALLY PRODUCT STRUCTURE OF INTERNAL SPACE AND SOME OF THE PROPERTIES IN HETEROTIC STRING ACTION. Chinese Physics C, 1987, 11(5): 614-619.
[16]	LI Zeng-Hai , MAO Nai-Feng , LIU Lan-Fen , SUN Qin-Ren . SPATIAL DISTRIBUTION OF MAGNETIC FIELD EXPRESSED BY THE FIELD ON MERIDIANAL PLANE. Chinese Physics C, 1986, 10(6): 730-737.
[17]	LI Yuan-Jie , ZHANG Duan-Ming . CHARGED BOSON BOUND STATES IN THE KERR-NEWMAN METRIC. Chinese Physics C, 1986, 10(4): 412-419.
[18]	HU Lian , GUO Shuo-Hong . A VARIATIONAL RESEARCH FOR HADRON SPECTRUM. Chinese Physics C, 1986, 10(3): 288-296.
[19]	ZHAO Guang-Ta , HUANG Chao-Shang . THE NEGATIVE METRIC THEORY FOR THE MASSIVE VECTOR MESON FIELD. Chinese Physics C, 1984, 8(1): 17-24.
[20]	Gao Chung-shou . MASS SPLITTINGS OF MESONS AND BARYONS IN COLOUR SPACE. Chinese Physics C, 1978, 2(1): 90-92.

Access

Get Citation

Wu Yong-shi and Lu Qi-keng. RIGHT TRANSLATION INVARIANT METRICS AND VARIATIONAL PRINCIPLES ON A PRINCIPAL BUNDLE——TREATED AS THE UNION OF SPACE-TIME AND AN INTERNAL SPACE[J]. Chinese Physics C, 1980, 4(3): 322-336.

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1979-03-13
Revised: 1900-01-01

Article Metric

Article Views(2095)
PDF Downloads(283)
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

RIGHT TRANSLATION INVARIANT METRICS AND VARIATIONAL PRINCIPLES ON A PRINCIPAL BUNDLE——TREATED AS THE UNION OF SPACE-TIME AND AN INTERNAL SPACE

Wu Yong-shi
Lu Qi-keng

Received Date: 1979-03-13
Accepted Date: 1900-01-01
Available Online: 1980-06-05

Abstract: In this paper, we discuss how to assign a metric on a principal bundle and howto rewrite the variational principles for a particle and for matter fields in an inva-riant from on the bundle in the principal-bundle formulation of gauge theories. Weshow that the right-translation invariant metric on the bundle must contain quantitieswhich transform exactly as gauge potentials, thus providing a new formalism for gaugefields. And we formulate the variational principle for a particle moving in the gaugefield as follows: The particle moves along a horizontal geodesic on the principalbundle. Starting from this we derive the Wong's equations of motion. Moreover, we elucidate the physical view-point which treats the bundle space asthe union of space-time and the internal space. Advantages of this viewpoint for un-derstanding the essentialities of gauge transformations and gauge invariance and forestablishing unified theories of gravitation and gauge fields are also discussed.