Construction of a Quantum Field Linked to the Coulomb Potential

  • Nicolas Privault
Conference paper
Part of the Progress in Probability book series (PRPR, volume 42)

Abstract

We construct a non-Gaussian field and its associated creation and annihilation operators, describing non-interacting bound states with no momentum in a Coulomb potential. The system is shown to behave quantum mechanically as a collection of coupled harmonic oscillators, allowing us to construct the field by injection into the quantum mechanical space of a free Gaussian field, and to study its time development.

Keywords

Covariance 

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References

  1. [1]
    P. Carmona. Généralisation de la loi de l’arc sinus et entrelacements de processus de Markov. Thèse, Université de Paris VI, 1994.Google Scholar
  2. [2]
    P. Feinsilver and R. Schott. Algebraic Structures and Operator Calculus, Vol I: Representations and Probability Theory, volume 241 of Mathematics and Its Applications. Kluwer Academic Publishers, Dordrecht, 1993.CrossRefGoogle Scholar
  3. [3]
    W. Feller. An Introduction to Probability Theory and its Applications, volume II. John Wiley and Sons, New York, 1966.Google Scholar
  4. [4]
    J. Glimm and A. Jaffe. Quantum Physics, a Functional Integral Point of View. Springer Verlag, Berlin/New-York, 1987.Google Scholar
  5. [5]
    T. Hida, H. H. Kuo, J. Potthoff, and L. Streit. White Noise, an infinite dimensional calculus. Kluwer Academic Publishers, Dordrecht, 1993.MATHGoogle Scholar
  6. [6]
    J. W. Pitman and M. Yor. A decomposition of Bessel bridges. Zeitschrift für Wahrsch., 59:425–457, 1982MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    N. Privault. Chaotic and variational calculus in discrete and continuous time for the Poisson process. Stochastics and Stochastics Reports, 51:83–109, 1994.MathSciNetMATHGoogle Scholar
  8. [8]
    N. Privault. A different quantum stochastic calculus for the Poisson process. Probability Theory and Related Fields, 105:255–278, 1996.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    D. Revuz and M. Yor. Continuous Martingales and Brownian Motion. Springer-Verlag, Berlin/New-York, 1994.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Nicolas Privault

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