De Broglie-Bohm Relativistic HVT

  • Andrey Anatoljevich Grib
  • Waldyr Alves RodriguesJr.

Abstract

In this ChapterM = (M, D,η), denotes Minkowski spacetime[1], i.e., M is a four dimensional manifold diffeomorphic to R 4, η is a Lorentzian metric of signature (1, 3) and D is the Levi-Civita connection of η. As is well known, under these conditions there exists a global coordinate chart 〈 x µ 〉 of the maximal atlas of M, such that there is a global basis ∂/∂x µ of TM (the tangent bundle) such thatl
$$ \eta \mu v = \eta (\partial /\partial {{x}^{\mu }},\partial /\partial {{x}^{v}}) = diag(1, - 1, - 1, - 1) $$
(11.1)

Keywords

Manifold Soliton Unal 

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References

  1. [1]
    R. K. Sachs and H. Wu, General Relativity for Mathematicians (Springer, New York, 1997).Google Scholar
  2. [2]
    D. Bohm and B. J. Hilley, Undivided Universe (Routledge, London and New York, 1993).Google Scholar
  3. [3]
    P. R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).CrossRefGoogle Scholar
  4. [4]
    W. A. Rodrigues Jr. and J. Y. Lu,On the existence of undistorted progressive waves (UPWs) of arbitrary speeds 0 < v < oo in nature, Found. Phys. 27(3) 453–508 (1997).MathSciNetCrossRefGoogle Scholar
  5. [5]
    W. A. Rodrigues Jr., Q. A. G. de Souza, J. Vaz Jr. and P. Lounesto, DiracHestenes spinor fields in Riemann-Cartan manifolds, Int. J. Theor. Phys. 35(9), 1849–1900 (1996).MATHCrossRefGoogle Scholar
  6. [6]
    A. Lasenby, S. Gull and C. Doran, in: Clifford (Geometrical) Algebras with Applications in Physics, Mathematics and Engineering, edited by W. E. Baylis (Birkhäuser, Boston, 1996), pp.147–169.Google Scholar
  7. [7]
    W. A. Rodrigues Jr., J. Vaz Jr, E. Recami and G. Sallesi,About zitterbewegung and electron structure, Phys. Lett. B 318(4), 623–628 (1993).MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    W. A. Rodrigues Jr. and J. Vaz Jr., in: Electron Theory and Quantum Electrodynamics, edited by J. P. Dowling (Plenum Publ. Corporation, New York, 1997), pp. 201–222.Google Scholar
  9. [9]
    W. A. Rodrigues Jr., J. Vaz Jr. and M. Paysic The Clifford bundle and the dynamics of the superparticle, Banach Center Publ., Polish Acad. Sci. 37, 295–314 (1996).Google Scholar
  10. [10]
    W. E. Baylis,, in: Clifford (Geometrical) Algebras with Applications in Physics, Mathematics and Engineering, edited by W. E. Baylis (Birkhäuser, Boston, 1996), pp.253–268.Google Scholar
  11. [11]
    H. Schmidt, Collapse of the state vector and PK effect, Found. Phys. 12(6) 565–581 (1982).ADSCrossRefGoogle Scholar
  12. [12]
    H. P. Stapp, Theoretical model of a purported empirical violation of the predictions of quantum theory, Phys. Rev. A 50(1), 18–22 (1994).MathSciNetGoogle Scholar
  13. [13]
    E. J. Squires, An experiment to test an explanation of a possible violation of quantum theory, Found. Phys. Lett. 8(6), 589–591 (1995).MathSciNetCrossRefGoogle Scholar
  14. [14]
    O. Costa de Beauregard, Macroscopic retrocausation, Found. Phys. Lett. 8(3), 287–291(1995).MathSciNetCrossRefGoogle Scholar
  15. [15]
    L. de Broglie, Non Linear Quantum Mechanics. A Causal Interpretation, Elsevier Publishing Co., Amsterdam, 1960.Google Scholar
  16. [16]
    L. Mackinnon, Nondispersive de Broglie wave packet, Found.Phys. 8(3–4), 3–4 (1978).ADSCrossRefGoogle Scholar
  17. [17]
    Ph. Gueret and J. P. Vigier, De Broglie wave particle duality in the stochastic interpretation of quantum mechanics—a testable physical assumption, Found. Phys. 12(11), 1057–1083 (1982);MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    Ph. Gueret and J. P. Vigier, Relativistic wave equations with quantum potential, 38(4),125–128 (1983).MathSciNetGoogle Scholar
  19. [19]
    H. Freidstadt, The causal formulation of quantum mechanics of particles, Nuovo Cimento 5(suppl.), 1–70 (1957).Google Scholar
  20. [20]
    A. O. Barut, Schrödinger’s interpretation of IF as a continuous charge distribution, Annalen der Phys. 45(7), 31–36 (1998).Google Scholar
  21. [21]
    A. O. Barut and N. Una, A new approach to bound-state quantum electrodynamics. 1. Theory, Physica A 142(1–3), 1–3 (1987).ADSCrossRefGoogle Scholar
  22. [22]
    A. O. Barut and J. P. Dowling, Quantum electrodynamics based on self-energy without 2nd quantization—the Lamb shift and long range Casimir-Polder-van der Walls forces near boundaries Phys. Rev. A 36(6), 2250–2556 (1987).Google Scholar
  23. [23]
    A. O. Barut, The revival of Schrödinger’s interpretation of quantum mechanics, Found. Phys. Lett. 1 (1), 47–56 (1988).MathSciNetCrossRefGoogle Scholar
  24. [24]
    P. Saari and K. Reivelt, Evidence for X-shaped propagation-invariant localized light waves, Phys. Rev. Lett. 79(21), 4135–4138 (1997).ADSCrossRefGoogle Scholar
  25. [25]
    E. Capelas de Oliveira and W. A. Rodrigues Jr., Superluminal electromagnetic waves in free space, Ann. der Physik 7(7–8), 7–8 (1998).ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Andrey Anatoljevich Grib
    • 1
  • Waldyr Alves RodriguesJr.
    • 2
  1. 1.State University of Economics and Finances of St. PetersburgSt. PetersburgRussia
  2. 2.State University of Campinas and Salesian UniversityCampinasBrazil

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