Abstract
Salam's SL(6,ℂ) gauge theory of strong interactions is generalized to one having GL(2f,ℂ) ⊗ GL(2c,ℂ or the affine extension thereof as structure group. The concept of fibre bundles and Lie-algebra-valued differential forms are employed in order to exhibit the geometrical structure of this gauge-model. Its dynamics is founded on a gauge-invariant Einstein-Dirac-type Lagrangian. The Heisenberg-Pauli-Weyl non-linear spinor equation generalized to a curved space-time of hadronic dimensions and Einstein-type field equations for the strong f-metric are then derived from variational principles. It is shown that the nonlinear terms are induced into the Dirac equation by Cartan's geometrical notion of torsion. It may be speculated that in this geometrical model extended particles are represented by f x c quarks which are (partially) Confined within geon-like objects.
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References
Anderson, D.L.T. (1971). J. Math. Phys. 12, 945.
Bjorken, J.D., and Drell, S.D. (1964) Relativistic Quantum Mechanics (Mc-Graw-Hill, San Francisco).
Cartan, E. (1922). Acad. Sci. Paris, Comptes Rend. 174, 593.
Cartan, E. (1923). Ann. École Norm. Sup. 40, 325.
Coleman, S. and Smarr, L. (1977). Commun. math Phys. 56, 1.
Deppert, W. and Mielke, E.W. (1979) “Localized Solutions of the non-linear Heisenberg-Klein-Gordon equation. In flat and exterior Schwarzschild space-time” Phys. Rev. D 20, 1303.
Fairchild, Jr., E.E. (1977) Phys. Rev. D 16, 2438.
Flanders, H. (1963). Differential Forms with Applications to Physical Sciences (Academic Press, New York).
Gell-Mann, M. and Ne'eman, Y. (1964). The Eightfold Way (Benjamin New York).
Gell-Mann, Ramond, P., and Slansky, R. (1978). Rev. Mod. Phys. 50, 721.
Hehl, F.W., and Datta, B.K. (1971). J. Math. Phys. 12, 1334.
Hehl, F.W., von der Heyde, P., Kerlick, G.D., and Nester, J.M. (1976). Rev. Mod. Phys. 48, 393
Heisenberg, W. (1966). Introduction to the Unified Field Theory of Elementary Particles (Wiley, London).
Heisenberg, W. (1974). Naturwissenschaften 61, 1.
Isham, C.J., Salam, A., and Strathdee, J. (1971). Phys. Rev. D 3, 867; (1973). Phys. Rev. D 8, 2600; (1974). Phys. Rev. D 9. 1702.
Isham, C.J. (1978). Proc. R. Soc. London. A. 364, 591.
Kobayashi, S., and Nomizu, K. (1963). Foundations of Differential Geometry, Vol. I. (Interscience, New York) (quoted as KN).
Muchar, K. (1965). Acta. Phys. Polon. 28, 695.
Lord, E.A., (1978). Phys. Lett. 65A. 1.
Mielke, E.W. (1977). Phys. Rev. Lett. 39, 530.
Misner, C.W., Thorne, K.S., and Wheeler, J.A. (1973). Gravitation (Freeman and Co., San Francisco), (quoted as MTW).
Rund, H., and Lovelock, D. (1972). Über. Deutsch. Math.-Verein, 74, 1.
Salam, A. (1973). In: Fundamental Interactions in Physics, edited by B. Kursunoglu et al. (Plenum, New York), p. 55.
Salam, A., and Strathdee, J. (1976). Phys. Lett. 61B, 375.
Salam, A., and Strathdee, J. (1978). Phys. Rev. D l18, 4596.
Trautman, A. (1972-73). Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 20, 185, 503, 895; 21, 345.
Weyl, H. (1929), Z. Physik 56, 330.
Weyl, H. (1950). Phys. Rev. 77, 699.
Wheeler, J.A. (1962). Geometrodynamics (Academic Press, New York).
Wheeler, J.A. (1971). In Cortona Symposium on “The Astrophysical Aspects of the Weak Interactions”, edited by L. Radicati (Academia Nazinale Dei Lincei, Roma) p. 133.
Yang, C.N., and Mills, R.L. (1954). Phys. Rev. 96, 191.
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Mielke, E.W. (1981). Gauge-theoretical foundation of color geometrodynamics. In: Doebner, HD. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Physics, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10578-6_27
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DOI: https://doi.org/10.1007/3-540-10578-6_27
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