link.springer.com

Dirac Theory in Hydrodynamic Form - Foundations of Physics

  • ️Fabbri, Luca
  • ️Fri May 12 2023

  • Pusey, M.F., Barrett, J., Rudolph, T.: On the reality of the quantum state. Nat. Phys. 8, 476 (2012)

    Article  Google Scholar 

  • Schrödinger, E.: Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807 (1935)

    Article  ADS  MATH  Google Scholar 

  • Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  ADS  MATH  Google Scholar 

  • Bohm, D., Aharonov, Y.: Discussion of experimental proof for the paradox of Einstein, Rosen, and Podolsky. Phys. Rev. 108, 1070 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  • Bell, J.S.: On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447 (1966)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • John Stewart Bell: On the Einstein Podolsky Rosen paradox. Phys. Phys. Fizika 1, 195 (1964)

    Article  MathSciNet  Google Scholar 

  • Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden variable theories. Phys. Rev. Lett. 23, 880 (1969)

    Article  ADS  MATH  Google Scholar 

  • Kochen, S., Specker, E.: The Problem of Hidden Variables in Quantum Mechanics. J. Math. Mech. 17, 59 (1968)

    MathSciNet  MATH  Google Scholar 

  • Cabello, A.: Interpretations of Quantum Theory: A Map of Madness–In Information and Quantum Mechanics. Cambridge University Press, Cambridge (2017)

    MATH  Google Scholar 

  • de Broglie, L.: La mécanique ondulatoire et la structure atomique de la matière et du rayonnement. J. Phys. Radium 8, 225 (1927)

    Article  MATH  Google Scholar 

  • de Broglie, L.: Sur l’introduction des idées d’onde-pilote et de double solution dans la théorie de l’électron de Dirac. C. R. Acad. Sci. 235, 557 (1952)

    MATH  Google Scholar 

  • Vigier, J.P.: Forces s’exerçant sur les lignes de courant usuelles des particules de spin \(0\), \(1/2\) et \(1\) en théorie de l’onde pilote. C. R. Acad. Sci. 235, 1107 (1952)

    MATH  Google Scholar 

  • Vigier, J.P.: Structures des micro-objets dans l’interpretation causale de la théorie des quanta. Ph.D. Thesis (1956)

  • Bohm, D.: A suggested interpretation of the quantum theory in terms of ‘Hidden’ Variables. Phys. Rev. 85, 166 (1952)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Takabayasi, Takehiko: On the formulation of quantum mechanics associated with classical pictures. Prog. Theor. Phys. 8, 143 (1952)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Bohm, D.: Comments on an article of Takabayasi concerning l. Prog. Theor. Phys. 9, 273 (1953)

    Article  ADS  MATH  Google Scholar 

  • Bohm, D., Schiller, R., Tiomno, J.: A causal interpretation of the Pauli equation (A and B). Nuovo Cimento 1, 48 and 67 (1955)

  • Takabayasi, T.: On the hydrodynamical representation of non-relativistic spinor equation. Prog. Theor. Phys. 12, 810 (1954)

    Article  ADS  MathSciNet  Google Scholar 

  • Holland, P.R.: The Dirac equation in the de Broglie-Bohm theory of motion. Found. Phys. 22, 1287 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  • Dürr, D., Munch-Berndl, K.: A hypersurface Bohm-Dirac theory. Phys. Rev. A 60, 2729 (1999)

    Article  ADS  Google Scholar 

  • Dürr, D., Goldstein, S., Norsen, T., Struyve, W., Zanghì, N.: Can Bohmian mechanics be made relativistic? Proc. R. Soc. Lond. A 470, 20130699 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  • Yvon, J.: Équations de Dirac-Madelung. J. Phys. Radium 1, 18 (1940)

    Article  MathSciNet  MATH  Google Scholar 

  • Takabayasi, T.: Relativistic hydrodynamics equivalent to the Dirac equation. Prog. Theor. Phys. 13, 222 (1955)

    Article  ADS  Google Scholar 

  • Takabayasi, T.: Hydrodynamical description of the Dirac equation. Nuovo Cimento 3, 233 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  • Takabayasi, T.: Relativistic hydrodynamics of the dirac matter. Prog. Theor. Phys. Supplement 4, 1 (1957)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Jakobi, G., Lochak, G.: Introduction des paramètres relativistes de Cayley-Klein dans la représentation hydrodynamique de l’équation de Dirac. C. R. Acad. Sci. 243, 234 (1956)

    MathSciNet  Google Scholar 

  • Jakobi, G., Lochak, G.: Decomposition en paramètres de Clebsch de l’impulsion de Dirac et interprétation physique de l’invariance de jauge des équations de la Mécanique ondulatoire. C. R. Acad. Sci. 243, 357 (1956)

    MathSciNet  Google Scholar 

  • Fabbri, L.: Spinors in polar form. Eur. Phys. J. Plus 136, 354 (2021)

    Article  Google Scholar 

  • Fabbri, L.: de Broglie-Bohm formulation of Dirac fields. Found. Phys. 52, 116 (2022)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Holland, Peter R.: The Quantum Theory of Motion. Cambridge University Press, Cambridge (1993)

    Book  Google Scholar 

  • Tumulka, R.: Foundations of Quantum Mechanics. Springer, Cham (2022)

    Book  MATH  Google Scholar 

  • Drezet, A.: Justifying Born’s rule \(P_{\alpha }=|\Psi _{\alpha }|^{2}\) using deterministic chaos, decoherence, and the de Broglie-Bohm quantum theory. Entropy 23, 1371 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  • Drezet, A.: Making sense of Born’s rule \(p_{\alpha }=|\!|\Psi _{\alpha }|\!|^{2}\) with the many-minds interpretation. Quant. Stud. Math. Found. 8, 315 (2021)

    Article  MathSciNet  Google Scholar 

  • Drezet, A.: Forewords for the special issue ‘Pilot-wave and beyond: Louis de Broglie and David Bohm’s quest for a quantum ontology’. Foundations of Physics (2022)

  • Holland, P.: Uniqueness of paths in quantum mechanics. Phys. Rev. A 60, 4326 (1999)

    Article  ADS  Google Scholar 

  • Fabbri, L.: Geometry, Zitterbewegung, Quantization. Int. J. Geom. Meth. Mod. Phys. 16, 1950146 (2019)

    Article  MathSciNet  Google Scholar 

  • Gondran, M., Gondran, A.: Replacing the singlet spinor of the EPR-B experiment in the configuration space with two single-particle spinors in physical space. Found. Phys. 46, 1109 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Bohm, D., Hiley, B.J.: The Undivided Universe: An Ontological Interpretation of Quantum Theory. Routledge, London (1993)

    Google Scholar