Abstract
An outline is given as to how gauge transformations in a frame fiber can be interpreted as defining various types of transport of a moving frame along a path. The cases of general linear, parallel, Lorentz, and other transport groups are examined in Minkowski space-time. A specific set of frame coordinates is introduced. A number of results are obtained including a generalization of Frenet-Serret transport, an extension of Fermi-Walker transport, a relation between frame spaces and certain types of Finsler space, and a derivation of a Kaluza-Klein type metric. Frame transport in general Riemannian space-time is also discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (Freeman, San Francisco, 1973), pp. 169 and 228.
H. Flanders,Differential Forms with Applications to the Physical Sciences (Dover, New York, 1989), p. 146.
L. A. Cordero, C. T. J. Dodson, and M. de Léon,Differential Geometry of Frame Bundles (Kluwer, Dordrecht, 1989).
é. Cartan,La Méthode du Repére Mobile, la Théorie des Groupes Continues et las Espaces Generalisées (Herman, Paris, 1935).
J. G. Vargas,Found. Phys. 22, 507 (1992).
J. Krause,Int. J. Theor. Phys. 12, 35 (1975).
J. F. Corum,J. Math. Phys. 18, 770 (1977).
D. Gregorash and G. Papini,Nuovo Cimento B 55, 37 (1980).
B. Gogala,Int. J. Theor. Phys. 19, 587 (1980).
H. Urbantke,Am. J. Phys. 58, 747 (1990).
R. G. Beil,Found. Phys. 23, 1587 (1993).
E. T. Newman and T. W. J. Unti,J. Math. Phys. 4, 1467 (1963).
P. A. Hogan and G. F. R. Ellis,Ann. Phys. (N.Y.) 195, 293 (1989).
A. Herdegen,Phys. Lett. A 144, 293 (1990).
B. L. Willis,J. Math. Phys. 32, 1400 (1991).
A. Lozado and P. L. Torres,J. Math. Phys. 30, 345 (1989).
P. S. Florides, J. McCrea, and J. L. Synge,Proc. R. Soc. London A 292, 1 (1966).
J. L. Synge,Ann. Math. 84, 33 (1970).
A. J. Hanson and T. Regge,Ann. Phys. (N.Y.) 87, 498 (1974).
J. L. Synge,Relativity: The General Theory (North-Holland, Amsterdam, 1960), p. 10.
B. R. Iyer and C. V. Vishveshwara,Phys. Rev. D 48, 5706 (1993).
M. Rivas,J. Math. Phys. 30, 318 (1989).
B. Mashhoon,Phys. Lett. A 139, 103 (1989).
F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Néeman,Found. Phys. 19, 1075 (1989).
D. Ivanenko and G. Sardanashvily,Phys. Rep. 94, 1 (1983).
R. G. Beil,Int. J. Theor. Phys. 32, 1019 (1993).
R. G. Beil,Int. J. Theor. Phys. 31, 1025 (1992).
R. Miron and T. Kawaguchi,Int. J. Theor. Phys. 30, 1521 (1991).
R. G. Beil,Int. J. Theor. Phys. 26, 189 (1987).
R. G. Beil,Int. J. Theor. Phys. 30, 1663 (1991).
R. Adler, M. Bazin, and M. Schiffer,Introduction to General Relativity (McGraw-Hill, New York, 1975).
P. R. Holland and C. Philipidis, inQuantum Implications: Essays in Honour of David Bohm, B. J. Hiley and F. D. Peat, eds. (RKP, London, 1987).
I. Vetharaniam and G. E. Stedman,Class. Quantum Gravit. 11, 1069 (1994).
J. G. Vargas,Found. Phys. 21, 379 (1991).
M. V. Atre and N. Mukunda,J. Math. Phys. 27, 2908 (1986).
C. MØller,K. Dan. Vidensk. Selsk., Mat. Fys. Skr. 1, No. 10 (1961).
H.-J. Treder,Ann. Phys. (Leipzig) 28, 283 (1972).
U. Bleyer,Ann. Phys. (Leipzig) 39, 203 (1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Beil, R.G. Moving frame transport and gauge transformations. Found Phys 25, 717–742 (1995). https://doi.org/10.1007/BF02059125
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02059125