The Quantum Potential in Particle and Field Theory Models

  • Ignazio LicataEmail author
  • Davide Fiscaletti
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)


As known, the Klein-Gordon equation describe the behaviour of relativistic spinless particles.


Clifford Algebra Equivalence Principle Quantum Potential Relativistic Quantum Field Theory Bohmian Interpretation 
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  1. 1.
    Holland, P.R.: Geometry of dislocated de Broglie waves. Found. Phys. 17(4), 345–363 (1987)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Shojai, A., Shojai, F.: About some problems raised by the relativistic form of de Broglie-Bohm theory of pilot wave. Phys. Scr. 64(5), 413–416 (2001)MathSciNetADSCrossRefzbMATHGoogle Scholar
  3. 3.
    Shojai, F., Shojai, A.: Understanding quantum theory in terms of geometry. arXiv:gr-qc/0404102 v1 (2004)Google Scholar
  4. 4.
    Bertoldi, G., Faraggi, A., Matone, M.: Equivalence principle, higher dimensional Moebius group and the hidden antisymmetric tensor of quantum mechanics. Class. Quantum Grav. 17, 3965 (2000)Google Scholar
  5. 5.
    Brown, H., Sjöqvist, E., Bacciagaluppi, G.: Remarks on identical particles in de Broglie-Bohm theory. Phys. Lett. A 251, 229–235 (1999)MathSciNetADSCrossRefzbMATHGoogle Scholar
  6. 6.
    Brown, H.: The quantum potential: the breakdown of classical sympletic symmetry and the energy of localisation and dispersion. arXiv:quant-ph/9703007 (1997)Google Scholar
  7. 7.
    Brown, H., Holland, P.: Simple applications of Noether’s first theorem in quantum mechanics and electromagnetism. Am. J. Phys. 72(1), 34 (2004)MathSciNetADSCrossRefzbMATHGoogle Scholar
  8. 8.
    Dewdney, C., Horton, G.: Relativistically invariant extension of the de Broglie-Bohm theory of quantum mechanics. J. Phys. A: Math. Gen. 35(47), 10117 (2002)MathSciNetADSCrossRefzbMATHGoogle Scholar
  9. 9.
    Holland, P.R.: New trajectory interpretation of quantum mechanics. Found. Phys. 38, 881–911 (1998)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Holland, P.R.: Hamiltonian theory of wave and particle in quantum mechanics I: Liouville’s theorem and the interpretation of the de Broglie-Bohm theory. Nuovo Cimento B 116, 1043–1070; Hamiltonian theory of wave and particle in quantum mechanics II: Hamilton-Jacobi theory and particle back-reaction. Nuovo Cimento B 116, 1143–1172 (2001)Google Scholar
  11. 11.
    Holland, P.R.: Causal interpretation of Fermi fields. Phys. Lett. A 128, 9–18 (1988)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Holland, P.R.: Uniqueness of conserved currents in quantum mechanics. Ann. Phys. 12(7/8), 446–462 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Holland, P.R.: The de Broglie-Bohm theory of motion and quantum field theory. Phys. Rep. 224(3), 95–150 (1993)MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Holland, P.R.: Implications of Lorentz covariance for the guidance equation in two-slit quantum interference. Phys. Rev. A 67, 062105 (2003)ADSCrossRefGoogle Scholar
  15. 15.
    Holland, P.R.: Computing the wavefunction from trajectories: particle and wave pictures in quantum mechanics and their relation. Ann. Phys. 315(2), 505–531 (2005)MathSciNetADSCrossRefzbMATHGoogle Scholar
  16. 16.
    Holland, P.R.: Constructing the electromagnetic field from hydrodynamic trajectories. Proc. R. Soc. A 461, 3659–3679 (2005)MathSciNetADSCrossRefzbMATHGoogle Scholar
  17. 17.
    Horton, G., Dewdney, C.: A non-local, Lorentz-invariant, hidden variable interpretation of relativistic quantum mechanics based on particle trajectories. J. Phys. A: Math. Gen. 34, 9871 (2001)MathSciNetADSCrossRefzbMATHGoogle Scholar
  18. 18.
    Horton, G., Dewdney, C.: A relativistically covariant version of Bohm’s quantum field theory for the scalar field. J. Phys. A: Math. Gen. 37, 11935 (2004)MathSciNetADSCrossRefzbMATHGoogle Scholar
  19. 19.
    Horton, G., Dewdney, C., Ne’eman, U.: de Broglie’s pilot-wave theory for the Klein–Gordon equation and its space-time pathologies. Found. Phys. 32(3), 463–476 (2002)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Horton, G., Dewdney, C., Nesteruk, A.: Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation. J. Phys. A: Math. Gen. 33, 7337 (2000)MathSciNetADSCrossRefzbMATHGoogle Scholar
  21. 21.
    Mostafazadeh, A., Zamani, F.: Conserved current densities, localisation probabilities, and a new global gauge symmetry of Klein-Gordon fields. arXiv:quant-ph/0312078 (2003)Google Scholar
  22. 22.
    Mostafazadeh, A.: Quantum mechanics of Klein-Gordon-type fields and quantum cosmology. Ann. Phys. 309(1), 1–48 (2003)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    Carroll, R.: Quantum Theory, Deformation, and Integrability. North-Holland, Amsterdam (2000)zbMATHGoogle Scholar
  24. 24.
    Carroll, R.: Integrable systems as quantum mechanics. arXiv:quant-ph/0309159 (2003)Google Scholar
  25. 25.
    Carroll, R.: (X, ψ) duality and enhanced dKdV on a riemann surface. Nucl. Phys. B 502(3), 561–593 (1997)ADSCrossRefzbMATHGoogle Scholar
  26. 26.
    Carroll, R.: On the whitham equations and (X, ψ) duality. Supersymmetry and integrable models. lecture notes in physics vol. 502, pp. 33–56. Springer lecture notes in physics (1998)Google Scholar
  27. 27.
    Faraggi, A., Matone, M.: The equivalence postulate of quantum mechanics. Int. J. Mod. Phys. A 15, 1869–2017 (2000)MathSciNetADSzbMATHGoogle Scholar
  28. 28.
    Matone, M.: The cocycle of quantum Hamilton-Jacobi equation and the stress tensor of CFT. Brazilian. J. Phys. 35(02A), 316–327 (2005)Google Scholar
  29. 29.
    Nikolic, H.: Covariant canonical quantization of fields and Bohmian mechanics. Eur. Phys. J. C 42(3), 365 (2005)MathSciNetADSCrossRefzbMATHGoogle Scholar
  30. 30.
    Nikolic, H.: Bohmian particle trajectories in relativistic bosonic quantum field theory. Found. Phys. Lett. 17(4), 363–380 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Nikolic, H.: Bohmian particle trajectories in relativistic fermionic quantum field. Found. Phys. Lett. 18(2), 123–138 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Nikolic, H.: Quantum determinism from quantum general covariance. Int. J. Mod. Phys. D15(2006), 2171–2176 (2006)MathSciNetADSCrossRefGoogle Scholar
  33. 33.
    Bohm, D., Hiley, B.J.: On the relativistic invariance of a quantum theory based on beables. Found. Phys. 21(2), 243–250 (1991)MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    Gull, S., Lasenby, A., Doran, C.: Electron paths, tunnelling and diffraction in the spacetime algebra. Found. Phys. 23(10), 1329–1356 (1993)MathSciNetADSCrossRefGoogle Scholar
  35. 35.
    Hiley, B.J., Callaghan, R.E.: The Clifford algebra approach to quantum mechanics B: the Dirac particle and its relation to the Bohm approach. arXiv:1011.4033v1 [math-ph] (2010)Google Scholar
  36. 36.
    Kaloyerou, P.N.: The causal interpretation of the electromagnetic field. Phys. Rep. 244(6), 287–358 (1994)MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    Valentini, A.: Signal-locality, uncertainty, and the subquantum H-theorem. I. Phys. Lett. A 156, 5–11 (1991)MathSciNetADSCrossRefGoogle Scholar
  38. 38.
    Nikolic, H.: The general-covariant and gauge-invariant theory of quantum particles in classical backgrounds. Int. J. Mod. Phys. D 12(3), 407 (2003)MathSciNetADSCrossRefzbMATHGoogle Scholar
  39. 39.
    Nikolic, H.: A general covariant concept of particles in curved background. Phys. Lett. B 527(1), 119–124 (2002)MathSciNetADSCrossRefzbMATHGoogle Scholar
  40. 40.
    Nikolic, H.: Erratum to: “a general covariant concept of particles in curved background”. Phys. Lett. B 529(3), 265 (2002)MathSciNetADSCrossRefGoogle Scholar
  41. 41.
    Nikolic, H.: There is no first quantization except in the de Broglie-Bohm interpretation. arXiv:quant-ph/0307179 (2003)Google Scholar
  42. 42.
    Nikolic, H.: Covariant many-fingered time Bohmian interpretation of quantum field theory. Phys. Lett. A348, 166–171 (2006)MathSciNetADSCrossRefGoogle Scholar
  43. 43.
    Nikolic, H.: Boson-fermion unification, superstrings, and Bohmian mechanics. Found. Phys. 39(10), 1109–1138 (2009)MathSciNetADSCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Institute for Scientific MethodologyPalermoItaly

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