Geometric Quantum Mechanics

  • E. Santamato
Part of the NATO ASI Series book series (NSSB, volume 144)


Since the advent of quantummechanics, there have been many attempts to provide it with a classical interpretation. Two approaches have received great attention in recent years: the Madelung-Bohm hydrodynamical formulation1 and the Feynès-Nelson stochastic formulation2 Unfortunately, notwithstanding their conceptual appeal, these approaches raised more problems than they resolved and failed in their principal intent: to shed some light on the physical mechanism responsible of the wavelike properties of matter. An odd mechanism, in fact, is inherent to both theories eliciting “a mysterious dependence of the individual on the statistical ensemble of which it is a member”3. This feed-back mechanism has no analog in newtonian mechanics nor in the theory of stochastic processes and has a purely quantum origin. It is evident, therefore, that both the Madelung-Bohm and the Feynès-Nelson “classical” formulations are more of appearance than substance.


Newtonian Mechanic Statistical Ensemble Geometric Quantum Classical Interpretation Quantum Origin 


  1. 1).
    E. Madelung,Z.Phys.,40,332,(1926);Google Scholar
  2. 1a).
    D. Bohm,Phys.Rev.,85,166,(1952);MathSciNetADSCrossRefGoogle Scholar
  3. 1b).
  4. 2).
    I. Feynès,Z.Phys.,132,81,(1952);ADSCrossRefGoogle Scholar
  5. 2a).
    E. Nelson,Phys.Rev.,150,1079,(1966).ADSCrossRefGoogle Scholar
  6. 3).
    H. Freistadt,Il Nuovo Cimento (suppl.),5,1,(1957).MathSciNetCrossRefGoogle Scholar
  7. 4).
    J.L. Synge, “Relativity: the General Theory” (North-Holland,Amsterdam,1960), Chap IV.MATHGoogle Scholar
  8. 5).
    E. Santamato,Phys.Rev.D,29,216,(1984);MathSciNetADSCrossRefGoogle Scholar
  9. 5a).
    J.Math.Phys.,25,2477,(1984);MathSciNetADSCrossRefGoogle Scholar
  10. 5a).
    Phys.Rev.D,32,2615,(1985).MathSciNetADSCrossRefGoogle Scholar
  11. 6).
    J. Ehlers, F.B.E. Pirani and B. Schild in “General Relativity” ed. by L. O’Raifeartaigh,(Oxford Univ.Press,1972).Google Scholar
  12. 7).
    N. Woodhouse, “Geometric Quantization”,(Oxford Univ.Press,1980).MATHGoogle Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • E. Santamato
    • 1
  1. 1.Dipartimento di Fisica Nucleare SMFAUniversità di NapoliNapoliItaly

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