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

  • 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.
  • 加载中
  • [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.
  • 加载中

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.
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. shu
Milestone
Received: 1979-03-13
Revised: 1900-01-01
Article Metric

Article Views(1858)
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

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Email This Article

Title:
Email:

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

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.

    HTML

Reference (1)

目录

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return