Communications in Mathematical Physics

, Volume 107, Issue 4, pp 543–552 | Cite as

Von Neumann algebras associated to quantum-mechanical constants of motion

  • A. Grossmann
  • J. Slawny


We discuss, in an abstract setting, the objects which appear in the process of separating out constants of motion of “quasimomentum type” in quantum mechanics of a finite number of degrees of freedom.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Finite Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    von Neumann, J.: Math. Ann.104, 570 (1931)Google Scholar
  2. 2.
    Mackey, G.W.: In: Functional analysis and related fields. Browder, F. (ed.). Berlin, Heidelberg, New York: Springer 1968Google Scholar
  3. 3.
    Grossmann, A.: In: Statistical mechanics and field theory. Sen, R.N., Weil, C. (eds.). New York: Halsted Press 1972Google Scholar
  4. 4.
    Slawny, J.: On the regular representation, von Neumann uniqueness theorem, and the 22-algebra of canonical commutation and anticommutation relations, Preprint TAUP-227 71, Tel Aviv University; and Simon, B.: pp. 67–76. In: Mathematics of contemporary physics. Streater, R. (ed.). New York: Academic Press 1972Google Scholar
  5. 5.
    Dixmier, J.: LesC*-algèbres et leurs représentations. Paris: Gauthier-Villars 1964Google Scholar
  6. 6.
    Kastler, D.: TheC*-algebras of a free boson field. I. Discussion of the basic facts. Commun. Math. Phys.1, 14 (1968)Google Scholar
  7. 7.
    Connes, A.: Ann. Math.109, 73 (1976)Google Scholar
  8. 8.
    Ruelle, D.: Statistical mechanics. New York: Benjamin 1969Google Scholar
  9. 9.
    Pontryagin, L.S.: Topological groups. New York: Gordon and Breach 1966Google Scholar
  10. 10.
    Bourbaki, N.: General topology. Paris: Hermann 1966Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • A. Grossmann
    • 1
  • J. Slawny
    • 2
  1. 1.Centre de Physique Théorique II, CNRSMarseilleFrance
  2. 2.Centre for Transport Theory and Mathematical PhysicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

Personalised recommendations