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\(U(2,2)\)-invariant spinorial geometrodynamics. (English) Zbl 0884.53073

The author offers a critism of Dirac theory which indicates that it involves some hidden action-at-a-distance concepts which are incompatible with local gauge theory, and a new conformal \(SU(2,2)\) symmetry in the theory of Dirac particles is suggested.
Contents include: introduction and motivations and objections to the Dirac theory; a second order model with internal \(U(2,2)\) symmetry; reduction of the internal symmetry to \(SL(2,\mathbb{C})\); dynamical reduction to \(SL(2,\mathbb{C})\) and \(GL(2,\mathbb{C})\); and special solutions and correspondence with the standard theory.

MSC:

53Z05 Applications of differential geometry to physics
83E05 Geometrodynamics and the holographic principle
15A66 Clifford algebras, spinors
81R25 Spinor and twistor methods applied to problems in quantum theory
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
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References:

[1] Hehl, F. W.; Nitsch, J.; Van der Heyde, P., Gravitation and the Poincaré Gauge Field Theory with Quadratic Lagrangians, (Held, A., General Relativity and Gravitation. One Hundred Years after the Birth of Einstein, vol. 1 (1980), Plenum Press: Plenum Press New York), 329, Chapter 11
[2] Hehl, F. W.; Mc Crea, J. D.; Mielke, E. W., Weyl Space-Time, the Dilatation Current, and Creation of Graviting Mass by Symmetry Breaking, (Exact Sciences and their Philosophical Foundations. Exact Sciences and their Philosophical Foundations, Vorträge des Internationalen Hermann-Weyl Kongress, Kiel (1985), Vertrag Peter Lang: Vertrag Peter Lang Frankfurt/Main, Bern, New York, Paris)
[3] Ivanenko, D. D.; Pronin, P. I.; Sardanashvily, C. A., Gauge Theory of Gravitation (1985), Naukowa Dumka: Naukowa Dumka Kiev, (in Russian)
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[8] Sławianowski, J. J., Rep. Math. Phys., 35, 1 (1995)
[9] J. J. Sławianowski: Fortschritte der Physik44; J. J. Sławianowski: Fortschritte der Physik44
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