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Geometrization of electromagnetism and gravity based on a finsler space-time with gauge symmetry-II

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Il Nuovo Cimento B (1971-1996)

An Erratum to this article was published on 01 August 1993

Summary

We investigate further the application of Finsler space-time and its gauge geometry to Maxwell’s and Yang-Mills’ theories. An important difference between gauge geometry and the conventional Finsler geometry is discussed. A formula for the total gauge covariant differentiation is obtained. The consistent mathematical properties of the metric gauge tensor, the metric connections and homogeneity conditions for gauge covariant differentiations are discussed and clarified. We calculate scalar curvature in the presence of a point charge. The physical curvature of the Finsler space-time is discussed from the field-theoretic viewpoint.

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References

  1. J. P. Hsu:Nuovo Cimento B,108, 183 (1993).

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  2. See, for example,W. Pauli:Theory of Relativity (Pergamon, London, 1958) (translated byG. Feld), p. 193.

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  3. J. P. Hsu, P. S. Jian andHui Lu: UMass Dartmouth preprint (1993). WhenJ k m is replaced by a known function, as shown in (3.8), the second equation in (29) of ref.[1] is to be replaced by\(J'_k = [J_m (\partial x^m /\partial x'^k ) - (\dot \partial _m lnU)(\partial \dot x^m /\partial x'^k )]\) (where\(J'_k = - (d/dt)(\dot \partial '_k \ln U)\)), which can be shown by direct calculations.

  4. H. Rund:The Differential Geometry of Finsler Spaces (Springer-Verlag, Berlin, 1959), pp. 3–5, 67–74;J. L. Synge:Transs. Am. Math. Soc.,27, 61 (1925);J. H. Taylor:Trans. Am. Math. Soc.,27, 246 (1925).

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  5. C. N. Yang:Phys. Rev. D,1, 2360 (1970).

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  6. G. Randers:Phys. Rev.,59, 195; (1941); see alsoG. S. Asanov:Finsler Geometry, Relativity and Gauge Theories (D. Reidel, Boston, Mass., 1985), pp. 72–75.

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Authors and Affiliations

  1. Physics Department, University of Massachusetts Dartmouth, 02747-2300, North Dartmouth, MA, USA

    J. P. Hsu

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  1. J. P. Hsu
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An erratum to this article is available at http://dx.doi.org/10.1007/BF02828742.

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Hsu, J.P. Geometrization of electromagnetism and gravity based on a finsler space-time with gauge symmetry-II. Il Nuovo Cimento B 109, 645–657 (1994). https://doi.org/10.1007/BF02728447

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  • DOI: https://doi.org/10.1007/BF02728447

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