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Fundamental length hypothesis in a Gauge theory context

  • Vladimir G. Kadyshevsky
Fiber Bundles and Extended Particle Structures
Part of the Lecture Notes in Physics book series (LNP, volume 94)

Abstract

The new gauge formulation of the electromagnetic interaction theory, containing the “fundamental length” ℓ as a universal scale like ħ and c, is worked out. A key part belongs to the 4-dimensional de Sitter p-space, with the curvature radius ħ/ℓc In the new approach the electromagnetic potential becomes a 5-vector associated with de Sitter group O(4.1). The extra fifth component, called the τ-photon, similar to scalar and longitudinal photons, does not correspond to an independent dynamical degree of freedom. Respectively, the new local gauge group is larger than the ordinary one and depends intrinsically on the fundamental length ℓ

The gauge invariant equations of motion, replacing the Dirac-Maxwell equations, are set up. The new formulation is minimal with respect to the 5-potential but is not so in terms of the usual 4-potential.As a result, the underlying physics looks much richer than the ordinary electromagnetic phenomena. The new scheme predicts the existence of the electric dipole moments for charged particles, leading to a direct violation of P- and CP-symmetries, and the new universal correction to the (g-2)-anomaly. Further, some new group of internal symmetry, SUτ(2), arises that can be used to describe the lie-symmetry of the electromagnetic interactions. It turns out that SUτ(2)-symmetry is violated by the 4-fermion type interaction, induced by τ-photons, with associated coupling constant ≈αℓ2. This novel interaction might give rise to the μe-mass difference and processes like μ → 3e, μ → eγ, etc.

In the limit ℓ → 0, the new field equations turn into the Dirac-Maxwell equations for the electron, muon and electromagnetic fields. So, one may consider this approach as a generalization in a profound way of the standard theory of electromagnetic interactions at small distances ≲ℓ (high energies ≲ 1/ℓ).

The upper bound for the fundamental length l is discussed taking into account the various experimental data.

Keywords

Electric Dipole Moment Electromagnetic Interaction Parity Violation Magnetic Dipole Moment Fundamental Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    G.V. Watagin, Zc. Phys. 88, 92 (1934).Google Scholar
  2. 2.
    W. Heisenberg, Zc. Phys. 101, 533 (1936); W. Heisenberg, Introduction to the Unified Field Theory of Elementary Particles, Inters. Publ. 1966.Google Scholar
  3. 3.
    M.A. Markov, JETP 10, 1311 (1940).Google Scholar
  4. 4.
    H. Snyder, Phys. Rev. 71, 38 (1947); 72, 68 (1947).Google Scholar
  5. 5.
    C.N. Yang, Phys. Rev. 72, 814 (1947).Google Scholar
  6. 6.
    M.A. Markov, Nucl. Phys. 10, 140 (1958); A.A. Komar and M.A. Markov, Nucl. Phys. 12, 190 (1959); M.A. Markov, Hyperons and K-mesons, GIFML, Moscow, 1958.Google Scholar
  7. 7.
    D.I. Blokhintsev, UFN 61, 137 (1957).Google Scholar
  8. 8.
    Yu. A. Gol'fand, JETP 37, 504 (1959); 43, 256 (1962); 44, 1248 (1963).Google Scholar
  9. 9.
    V.G. Kadyshevsky, JETP 41, 1885 (1961), AN USSR Doklady, 147, 588, 1336 (1962).Google Scholar
  10. 10.
    I.E. Tamm, Proceedings of XII International Conference on High Energy Physics, vol. II, p. 229, Atomizdat, Moscow (1964); Proceedings of Inter. Confer. on Elementary Particles, Kyoto (1965).Google Scholar
  11. 11.
    R.M. Mir-Kasimov, JETP 49, 905, 1161 (1965); 52, 533 (1967).Google Scholar
  12. 12.
    D.A. Kirzhnits, UFN 90, 129 (1966).Google Scholar
  13. 13.
    A.N. Leznov, JINR preprint P2-3590, p. 52 (1967).Google Scholar
  14. 14.
    D.I. Blokhintsev, “Space and Time in Microworld,” Moscow, Nauka, 1970.Google Scholar
  15. 15.
    G.V. Efimov, Particles and Nuclei, I No. 1, 256 (1970); 5, No. 1, 223 (1974).Google Scholar
  16. 16.
    M.A. Solov'ev and V. Ya. Feinberg, in “Non-local, non-linear and non-renormalizable theories,” D2-9788, JINR, Dubna (1976).Google Scholar
  17. 17.
    S. Fubini, CERN preprint TH 2129-CERN (1976).Google Scholar
  18. 18.
    J.D. Bjorken, Proceedings of B. Lee Memorial Conference (to be published).Google Scholar
  19. 19.
    V.G. Kadyshevsky, JINR preprint P2-5717, Dubna (1971).Google Scholar
  20. 20.
    V.G. Kadyshevsky, in the book “Problems of Theoretical Physics” dedicated to the memory of I.E. Tamm, Moscow, Nauka, 1972; in “Non-local, Non-linear and Non-renormalizable Theories,” D2-7161, Dubna (1973).Google Scholar
  21. 21.
    A.D. Donkov, V.G. Kadyshevsky, M.D. Mateev and R.M. Mir-Kasimov, Bulgar. Journ. of Physics 1, 58, 150, 233 (1974); 2, 3 (1975); Proceedings of Internat. Conference on Mathemat. Problems of Quantum Field Theory and Quantum Statistics, pp. 85–129, Moscow, Nauka (1975); JINR preprint E2-7936, Dubna (1974).Google Scholar
  22. 22.
    R.M. Mir-Kasimov, “Axiomatic Quantum Field Theory and de Sitter momentum space,” in P1,2-7642, JINR, Dubna (1973).Google Scholar
  23. 23.
    V.G. Kadyshevsky, M.D. Mateev and R.M. Mir-Kasimov, JINR preprints: E2-8892, P2-8877, Dubna (1975).Google Scholar
  24. 24.
    V.G. Kadyshevsky, “Fundamental length as a new scale in quantum field theory,” in D1,2-9342, Dubna (1975).Google Scholar
  25. 25.
    A.D. Donkov, V.G. Kadyshevsky, M.D. Mateev and R.M. Mir-Kasimov, in “Non-local, Nonlinear and Non-renormalizable theories,” D2-9788, Dubna (1976); Proceedings of the XVIII International Conference on High Energy Physics, Tbilisi, p. A5-1, D1,2-10400, Dubna (1977).Google Scholar
  26. 26.
    M.D. Mateev, “Processes at High Energies and Fundamental Length Hypothesis,” in D2-10533, p. 257, Dubna (1977).Google Scholar
  27. 27.
    I.P. Volobuyev, TMF 28, 331 (1976).Google Scholar
  28. 28.
    R.M. Mir-Kasimov, I.P. Volobuyev, Acta Physica Polonica B9, 2 (1978).Google Scholar
  29. 29.
    V.G. Kadyshevsky, M.D. Mateev, R.M. Mir-Kasimov and I.P. Volobuyev, JINR preprint, E210860 (1977).Google Scholar
  30. 30.
    V.G. Kadyshevsky, Fermilab-Pub-78/22-THY, Nuclear Physics (in press).Google Scholar
  31. 31.
    V.G. Kadyshevsky, Fermilab-Pub-78/70-THY, Annals of Physics (in press).Google Scholar
  32. 32.
    F.L. Shapiro, UFN, 95, 145 (1968).Google Scholar
  33. 33.
    L. Barkov, Parity Violation in Bi-atoms, XIX Int. Conference on High Energy Physics, Tokyo, 1978.Google Scholar
  34. 34.
    R.E. Taylor, Parity Violation in Polarized eD-Scattering, XIX Int. Conf. on High Energy Physics, Tokyo, 1978.Google Scholar
  35. 35.
    M.C. Weisskopf, et al., Phys. Rev. Lett. 21, 1645 (1968); T. S. Stein, et al., Phys. Rev. 186, 39 (1969).Google Scholar
  36. 36.
    M.A. Player and P.G.H. Sandars, J. Phys. B3, 1620 (1970).Google Scholar
  37. 37.
    P.G.H. Sandars and R.M. Sternheimer, Phys. Rev. All, 473 (1975).Google Scholar
  38. 38.
    B.V. Vasiliev, E.V. Kolycheva, JINR preprint, P14-10948 (1977).Google Scholar
  39. 39.
    L.D. Landau, JETP, 32, 405 (1957).Google Scholar
  40. 40.
    M.A. Markov, JETP 51, 878, 1966; Progress of Theor. Phys., H. Yukawa Suppl., p. 85 (1965).Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Vladimir G. Kadyshevsky
    • 1
  1. 1.Fermi National Accelerator LaboratoryBatavia

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