Abstract
A theory has been presented previously in which the geometrical structure of a real four-dimensional space time manifold is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group. The group enlargement was accomplished by including those transformations to anholonomic coordinates under which conservation laws are covariant statements. Field equations have been obtained from a variational principle which is invariant under the larger group. These field equations imply the validity of the Einstein equations of general relativity with a stress-energy tensor that is just what one expects for the electroweak field and associated currents. In this paper, as a first step toward quantization, a consistent Hamiltonian for the theory is obtained. Some concluding remarks are given concerning the need for further development of the theory. These remarks include discussion of a possible method for extending the theory to include the strong interaction.
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REFERENCES
Bade, W. L. and Jehle, H. (1953). An introduction to spinors. Reviews of Modern Physics 25, 714.
Barut, A. O. (1980). Electrodynamics and Classical Theory of Fields and Particles, 1st edn., Dover, New York, p. 11.
Bergmann, P. G. and Goldberg, I. (1955). Dirac bracket transformation in phase space. Physical Review 98, 531.
Dirac, P. A. M. (1930). The Principles of Quantum Mechanics, Cambridge University Press, Cambridge, Preface to First Edition.
Dirac, P. A. M. (1964). Lectures on Quantum Mechanics, Academic Press, New York.
Eddington, A. E. (1924). The Mathematical Theory of Relativity, 2nd edn., Cambridge University Press, Cambridge, p. 222.
Einstein, A. (1928a). Riemanngeometrie mit Aufrechterhaltung des Begriffes des Fernparallelismus. Preussischen Akademie der Wissenshaften, Phys.-math. Klasse, Sitzungsberichte 1928, 217.
Einstein, A. (1928b). Neue Möglichkeit für eine einheitliche Feltheorie von Gravitation und Elektrizität. Preussischen Akademie der Wissenshaften, Phys.-math. Klasse, Sitzungsberichte 1928, 224.
Einstein, A. (1949). In Albert Einstein: Philosopher-Scientist, Vol. I, P. A. Schilpp, ed. Harper, New York, p. 89.
Eisenhart, L. P. (1925). Riemannian Geometry, Princeton University Press, Princeton, NJ, p. 97.
Henneaux, M. and Teitelboim, C. (1992). Quantization of Gauge Systems, Princeton University Press, Princeton, NJ.
Loos, H. G. (1963). Spin connection in general relativity. Annals of Physics 25, 91.
Misner, C. (1957). Feynman quantization of general relativity. Reviews of Modern Physics 29, 497-509.
Moriyasu, K. (1983). An Elementary Primer for Gauge Theory, World Scientific, Singapore, p. 110.
Nakahara, M. (1990). Geometry, Topology and Physics, Adam Hilger, New York, p. 344.
Pandres, D., Jr. (1962). On forces and interactions between fields. Journal of Mathematical Physics 3, 602.
Pandres, D., Jr. (1981). Quantum unified field theory from enlarged coordinate transformation group. Physical Review D 24, 1499.
Pandres, D., Jr. (1984a). Quantum unified field theory from enlarged coordinate transformation group. II. Physical Review D 30, 317.
Pandres, D., Jr. (1984b). Quantum geometry from coordinate transformations relating quantum observers. International Journal of Theoretical Physics 23, 839.
Pandres, D., Jr. (1995). Unified gravitational and Yang—Mills fields. International Journal of Theoretical Physics 34, 733.
Pandres, D., Jr. (1998). Gravitational and electroweak interactions. International Journal of Theoretical Physics 37, 827-839.
Pandres, D., Jr. (1999). Gravitational and electroweak unification. International Journal of Theoretical Physics 38, 1783-1805.
Rosenfeld, I. (1930). “Zur Quantelung der Wellen felder,” Annalen der Physik, 5, 113.
Salam, A. (1968). Weak and electromagnetic interactions. In Proceedings of the 8th Nobel Symposium on Elementary Particle Theory, N. Svartholm, ed., Almquist Forlag, Stockholm, p. 367.
Schouten, J. A. (1954). Ricci-Calculus, 2nd edn., North-Holland, Amsterdam, p. 99ff.
Schrödinger, E. (1960). Space—Time Structure, Cambridge University Press, Cambridge, pp. 97, 99.
Schwarz, J. (1988). In Superstrings: A Theory of Everything? P. C. W. Davis, and J. Brown, eds., Cambridge University Press, Cambridge, p. 70.
Sundermeyer, K. (1982). Constrained Dynamics, Springer-Verlag, Berlin.
Synge, J. L. (1960). Relativity: The General Theory, North-Holland, Amsterdam, pp. 14, 357.
Weber, J. (1961). General Relativity and Gravitational Waves, Interscience, New York, p. 147.
Weinberg, S. (1967). A model of leptons. Physical Review Letters 19, 1264.
Weinberg, S. (1995). The Quantum Theory of Fields, Vol. I, Cambridge University Press, Cambridge.
Weinberg, S. (1996). The Quantum Theory of Fields, Vol. II, Cambridge University Press, Cambridge.
Weitzenböck, R. (1928). Differentialivarianten in der Einsteinschen Theorie de Fernparallelismus. Preussischen Akademie der Wissenshaften, Phys.-math. Klasse, Sitzungsberichte 1928, 466.
Witten, E. (1988). In Superstrings: A Theory of Everything? P. C. W. Davis, and J. Brown, eds., Cambridge University Press, Cambridge, p. 90.
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Pandres, D., Green, E.L. Unified Field Theory from Enlarged Transformation Group. The Consistent Hamiltonian. International Journal of Theoretical Physics 42, 1849–1873 (2003). https://doi.org/10.1023/A:1026147725039
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DOI: https://doi.org/10.1023/A:1026147725039