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Fields in nonaffine bundles. I. The general bitensorially gauge-covariant differentiation procedure
Phys. Rev. D 33, 983 – Published 15 February, 1986
DOI: https://doi.org/10.1103/PhysRevD.33.983
Abstract
The standard covariant differentiation procedure for fields in vector bundles is generalized so as to be applicable to fields in general nonaffine bundles in which the fibers may have an arbitrary nonlinear structure. In addition to the usual requirement that the base space should be flat or endowed with its own linear connection Γ, and that there should be an ordinary gauge connection A on the bundle, it is necessary to require also that there should be an intrinsic, bundle-group-invariant connection Γ^ on the fiber space. The procedure is based on the use of an appropriate primary-field- (i.e., section-) dependent connector ω that is constructed in terms of the natural fiber-tangent-vector realization A of the gauge connection. The application to gauged-harmonic mappings will be described in the following article.
See Also
References (5)
- Y. Choquet-Bruhat, C. Morette-DeWitt, and M. Bleck-Dillard, Physical Mathematics—Analysis on Manifolds (North-Holland, Amsterdam, 1977).
- C. W. Misner, Phys. Rev. D 18, 4510 (1978).
- B. Carter, in Non-Linear Equations in Classical and Quantum Field Theory, edited by N. Sanchez (Lecture Notes in Physics, Vol. 223) (Springer, Heidelberg, 1985), p. 72.
- B. Carter, in Recent Developments in Gravitation, Carge`se, 1978, edited by M. Lévy and S. Deser (Plenum, New York, 1979).
- K. Yano, The Theory of Lie Derivatives and its Applications (North-Holland, Amsterdam, 1957).