Abstract
Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of “gauge” transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.
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REFERENCES
R. Maartens and D. R. Taylor, “Lifted transformations on the tangent bundle, and symmetries of particle motion,” Int. J. Theor. Phys. 32, 143(1993).
R. G. Beil, “Moving frame transport and gauge transformations”, Found. Phys. 25, 717(1995).
R. G. Beil, “Finsler and Kaluza–Klein gauge theories”, Int. J. Theor. Phys. 32, 1021(1993).
G. S. Asanov, Finsler Geometry, Relativity, and Gauge Theories (Reidel, Dordrecht, 1985).
P. L. Antonelli, R. S. Ingarden, and M. Matsumoto, The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology (Kluwer Academic, Dordrecht, 1993).
D. Bao, S.-S. Chern, and Z. Shen, An Introduction to Riemann-Finsler Geometry (Springer, New York, 2000).
R. Miron and M. Anastasiei, The Geometry of Lagrange Spaces: Theory and Applications (Kluwer Academic, Dordrecht, 1994).
R. G. Beil, “Electroweak symmetry on the tangent bundle”, Int. J. Theor. Phys. 40, 591(2001).
P. R. Holland, “Geometry of dislocated de Broglie waves”, Found. Phys. 17 (1987).
I. Bucataru, “Nonholonomic frames in Finsler geometry”, Balkan J. Geom. 7, 13(2002).
R. G. Beil, “New class of Finsler metrics”, Int. J. Theor. Phys. 28, 659(1989).
R. G. Beil, “Finsler gauge transformations and general relativity”, Int. J. Theor. Phys. 31, 1025(1992).
M. Anastasiei and H. Shimada, “The Beil metrics associated to a Finsler space”, Balkan. J. Geom. 3, 1(1998).
P. C. Stavrinos, D. Nikolopoulos, and N. Prezas, “Finslerian metric based on the gravitational and electromagnetic fields”, in Proceedings of the IV and V Romanian National Conferences on Theoretical Physics, General Relativity, and Gravitation, Vol. 4 and 5 (Bistrita, Romania, 1997).
R. S. Ingarden, M. Matsumoto, and L. Tamassy, “Vector field relative Finsler space in two physical examples”, Nonlinear World 4, 85(1997).
V. Balan, P. C. Stavrinos, and K. Trencevski, “Weak gravitational models based on Beil metrics”, in Proceedings of the Conference of Applied Differential Geometry (Thessaloniki, Greece, 2000).
V. Balan, “Synge–Beil and Riemann–Jacobi jet structures with applications to physics”, to be published.
R. G. Beil, “Equations of motion from Finsler geometric methods”, in Finsler Geometries, A Meeting of Minds, P. L. Antonelli, ed. (Kluwer Academic, Dordrecht, 2000).
R. G. Beil, “Electrodynamics from a metric”, Int. J. Theor. Phys. 26, 189(1987).
D. Ivanenko and G. Sardanashvily, “The gauge treatment of gravity”, Phys. Rep. 94, 1(1983).
R. G. Beil, “Notes on a new Finsler metric function”, Balkan J. Geom. 2, 1(1997).
R. G. Beil,“Comparison of unified field theories,” Tensor, N. S. 56, 175(1995).
R. G. Beil, “Finsler geometry and a unified field theory,” in Finsler Geometry, D. Bao, S. S. Chern, and Z. Shen, eds. (American Mathematical Society, Providence, 1996).
D. Bao and C. Robles, “The spray curvature of a Randers metric”, unpublished notes.
R. S. Ingarden, “Differential geometry and physics”, Tensor, N. S. 30, 201(1976).
R. G. Beil, “Poincare transport of frames”, Found. Phys. 25, 1577(1995).
P. C. Stavrinos and P. Manouselis, “Tensor and spinor equivalence on generalized metric tangent bundles”, Balkan J. Geom. 2, 119(1997).
J. G. Vargas and D. G. Torr, “Quantum Clifford algebra from classical differential geometry”, J. Math. Phys. 43, 1353(2002).
H. E. Brandt,“Quantum fieldsinthe spacetime tangent bundle,” Found. Phys. Lett. 11, 265(1998).
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Beil, R.G. Finsler Geometry and Relativistic Field Theory. Foundations of Physics 33, 1107–1127 (2003). https://doi.org/10.1023/A:1025689902340
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DOI: https://doi.org/10.1023/A:1025689902340