As a part of an attempt to geometrize physics, internal symmetries in the covariant classification of matter by itsT μυ type are considered in relation to phase transformations generated by complex and quaternionic structures on space-time. The Rainich theory of electromagnetism and neutrinos is compared with the theory ofU(1) ×SO(1, 3) torsional gauge fields, and extended to the quaternionic case. It is shown by the Kostant technique of geometric quantization that complex and quaternionic phase transformations for an Einstein space are associated with one-dimensional and three-dimensional harmonic oscillators.
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Belavin, A. A., Polyakov, A. M., Schwarz, A. S., and Tyupkin, Yu. S. (1975).Physics Letters,59B, 85.
Bonan, E. (1967).Cahiers de Topologie et Géométrie Différentielle,9, 385.
Collinson, C. D., and Shaw, R. (1972).International Journal of Theoretical Physics,6, 347.
Fock, V. (1929).Zeitschrift für Physik,57, 261.
Hestenes, D. (1967).Journal of Mathematical Physics,8, 798.
Hestenes, D. (1975).Journal of Mathematical Physics,16, 556.
Inomata, A., and McKinley, W. A. (1965).Physical Review,140B, 1467.
Inomata, A., and McKinley, W. A. (1971).Relativity and Gravitation, C. G. Kuper and A. Peres, eds., p. 199. Gordon and Breach, New York.
Isham, C. J., Salam, A., and Strathdee, J. (1971).Annals of Physics (New York),62, 98.
Ishihara, S. (1974).Journal of Differential Geometry,9, 483.
Kobayashi, S. (1972).Transformation Groups in Differential Geometry. Springer Verlag, Berlin.
Kostant, B. (1970a).Lecture Notes in Physics,6, 237.
Kostant, B. (1970b).Lecture Notes in Mathematics,170, 87.
Kraines, V. Y. (1966).Transactions of the American Mathematical Society,122, 357.
Lloyd-Evans, D. J. R. (1976a).Nuovo Cimento Letters,16, 321, 325.
Lloyd-Evans, D. J. R. (1976b).International Journal of Theoretical Physics,15, 427.
Lloyd-Evans, D. J. R. (1977).General Relativity and Gravitation,8, 353.
Lloyd-Evans, D. J. R. (1979).International Journal of Theoretical Physics, to be published.
Ludwig, G. (1970).Communications in Mathematical Physics,17, 98.
Misner, C. W., and Wheeler, J. A. (1957).Annals of Physics (New York),2, 525.
Petrov, A. S. (1969).Einstein Spaces. Pergamon Press, London.
Plebanski, J. (1964).Acta Physica Polonica,26, 963.
Rainich, G. Y. (1925).Transactions of the American Mathematical Society,27, 106.
Rodichev, V. I. (1961).Journal of Experimental and Theoretical Physics,13, 1029.
Sarfatti, J. (1975).Foundations of Physics,5, 301.
Segal, I. (1960).Journal of Mathematical Physics,1, 468.
Simms, D. J., and Woodhouse, N. M. J. (1976).Lecture Notes in Physics,53, 1.
Yano, K. (1965).Differential Geometry on Complex and Almost Complex Spaces. Pergamon Press, London.
Yano, K., and Ako, M. (1973).Journal of Differential Geometry,8, 341.
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Lloyd-Evans, D.J.R. Geometric quantization and internal symmetry. Int J Theor Phys 18, 193–212 (1979). https://doi.org/10.1007/BF00670396
- Field Theory
- Elementary Particle
- Phase Transformation
- Quantum Field Theory
- Harmonic Oscillator