Quantum model of geometric extension

G.L. Stavraki1

Abstract

We construct a model of space-time structure on the basis of the operator field theory. Instead of a world point, the carrier of possible local events is assumed to be a universal supermatrix complex U which comprises a complete set of local field operators. A basic element of extension is described in the model by an equation of a special commutator algebra closed on two such local complexes U1 and U2, "nearest" in the lightlike connection and connected by one vertex of virtual interaction of fields. The corresponding causal relationship is interpreted in the classical picture of the description as a lightlike line closed as a "figure-of-eight" loop, and in the quantum picture as a symmetric T-time jump (reflection) between the nearest local past and future. The discrete nature of the constructed "quantum proximity" equation, containing the gravitational constant, is associated with the existence of a local curvature on the Planck scale. The algebraic closedness of the fundamental equation suggests that the charge symmetry group should be E6 with non-standard representations for fermionic and scalar fields. The model also makes it possible to consider the symmetric two-way time flow as a chain of local T-reflections.

References

  1. G. L. Stavraki, Teor. Mat. Fiz. 84, 339 (1990).
  2. F. A. Berezin, Method of Second Quantization (Academic Press, New York, 1966) [Russian original: Nauka, Moscow, 1965].
  3. G. L. Stavraki, in: International School on Theoretical Physics. High-Energy Physics and Elementary Particle Theory, Yalta, 1966. Naukova Dumka, Kiev, 1967, pp. 296-312.
  4. J. Wess and B. Zumino, Nucl. Phys. B 70, 39 (1974).
  5. J. Beem and P. Ehrlich. Global Lorentzian Geometry. Marcel Dekker, JNC, New York and Basel, 1981.
  6. R.F. Streater and A.S. Wightman. PCT, Spin and Statistics and All That. W.A. Benjamin, JNC, N.Y., 1964.
  7. V. De Alfaro, S. Fubini, G. Furlan, and C. Rossetti. Currents in Hadron Physics. North Holland Publ. Comp., Amst.-Lond., 1973.
  8. B. DeWitt. Supermanifolds. Cambridge University Press, 1984.
  9. G. L. Stavraki, Grav. & Cosmol. 12 227 (2006).
  10. S. W. Hawking, Nucl. Phys. B 114, 349 (1978).
  11. N. Bourbaki. Group et algebras de Lie. Chapitre IV-VI, Fascicule XXXIV. Herman, 1968. Chapitre VII-VIII, Fascicule XXXVIII, Herman, 1975.
  12. Y. Achiman and B. Stech, Phys. Lett. B 77, 389 (1978).
  13. S. Coleman and E. Weinberg, Phys. Rev. D 7, 1888 (1973).
  14. G. L. Stavraki, Model of Space-Time as a Virtually-Field Structure on Locally Light-Like Causal Relationships. URSS, Moscow, 2008 (in press).
For more information about this paper please visit Springer's Home Page of this paper.



Back to The Contents Page