Letters in Mathematical Physics

, Volume 28, Issue 2, pp 155–164 | Cite as

The extremal microscopic coherent boson states

  • Reinhard Honegger
Article

Abstract

In a recent paper, the Fock-normal (=microscopic) fully-coherent statesL L (∞) (L denotes the factorizing linear form) have been completely characterized, and the existence of nonpure elements in the extreme boundary of the weak-*-compact, convex setL L has been shown. This letter is devoted to an analysis of the extremal fully-coherent states, especially those which are not pure states. An affine isomorphism is constructed betweenL L (∞) and a certain convex subset of the normal completely positive maps on the bounded operators on Fock space. Then the extreme boundary ofL L (∞) is determined by results and techniques from the theory of completely positive operators.

Mathematics Subject Classifications (1991)

81V80 47D45 46N55 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Glauber, R. J., The quantum theory of optical coherence,Phys. Rev. 130, 2529–2539 (1963); Coherent and incoherent states of the radiation field,Phys. Rev. 131, 2766-2788 (1963); C. de Witt, A. Blandin and C. Cohen-Tannoudji (eds),Quantum Optics and Electronics, Les Houches 1964, Gordon and Breach, New York, 1965.Google Scholar
  2. 2.
    Honegger, R. and Rapp, A., General Glauber coherent states on the Weyl algebra and their phase integrals,Physica A 167, 945–961 (1990).Google Scholar
  3. 3.
    Honegger, R. and Rieckers, A., The general form of non-Fock coherent boson states,Publ. RIMS Kyoto Univ. 26, 397–417 (1990).Google Scholar
  4. 4.
    Honegger, R. and Rieckers, A., First order coherent boson states,Helv. Phys. Acta 65, 965–984 (1992).Google Scholar
  5. 5.
    Honegger, R. and Rieckers, A., On higher order coherent states on the Weyl Algebra,Lett. Math. Phys. 24, 221–225 (1992).Google Scholar
  6. 6.
    Titulaer, U. M. and Glauber, R. J., Density operators for coherent fields,Phys. Rev. 145, 1041–1050 (1966).Google Scholar
  7. 7.
    Honegger, R., The general form of the microscopic coherent states, Preprint, Tübingen, 1992.Google Scholar
  8. 8.
    Stinespring, W. F., Positive functions on C*-algebras,Proc. Amer. Math. Soc. 6, 211–216 (1955).Google Scholar
  9. 9.
    Kümmerer, B., Construction and structure of Markov dilations onW *-algebras, Postdoctoral thesis, Tübingen, 1988.Google Scholar
  10. 10.
    Kraus, K., General state changes in quantum theory,Ann. Phys. 64, 311–335 (1971).Google Scholar
  11. 11.
    Choi, M.-D., Completely positive linear maps on complex matrices,Linear Algebra Appl. 10, 285–290 (1975).Google Scholar
  12. 12.
    Arveson, W. B., Subalgebras of C*-algebras,Acta Math. 123, 141–224 (1969).Google Scholar
  13. 13.
    Bratteli, O. and Robinson, D. W.,Operator Algebras and Quantum Statistical Mechanics, Vol. II. Springer, Berlin, 1981.Google Scholar
  14. 14.
    Reed, M. and Simon, B.,Methods of Modern Mathematical Physics I; Functional Analysis, Academic Press, New York, 1980.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Reinhard Honegger
    • 1
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenGermany

Personalised recommendations