Advertisement

Stochastic Isometries in Quantum Mechanics

  • P. Busch
Article

Abstract

The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and symmetry transformations. Here a characterization of the isometric stochastic maps is given and possible physical applications are indicated.

Hilbert space trace class state operator stochastic map isometry quantum mechanics reversibility 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bargmann, V.: Notes on Wigner's theorem on symmetry operations, J. Math. Phys. 5 (1964), 862–868.Google Scholar
  2. 2.
    Busch, P.: Quantum extensions of quantum statistical models, Preprint, 1998.Google Scholar
  3. 3.
    Busch, P. and Quadt, R.: Operational characterization of irreversibility, Report Series, Department of Mathematics, University of Hull, 1998.Google Scholar
  4. 4.
    Cassinelli, G., DeVito, E., Lahti, P. J. and Levrero, A.: Symmetry groups in quantum mechanics and the theorem of Wigner on the symmetry transformations, Rev. Math. Phys. 9 (1997), 921–941.Google Scholar
  5. 5.
    Davies, E. B.: Quantum Theory of Open Systems, Academic Press, New York, 1976.Google Scholar
  6. 6.
    Emch, G. G.: Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley, New York, 1972.Google Scholar
  7. 7.
    Kadison, R. V.: Transformations of states in operator theory and dynamics, Topology 3(Suppl. 2) (1965), 177–198.Google Scholar
  8. 8.
    Kadison, R. V.: Isometries of operator algebras, Ann. of Math. 54 (1951), 325–338.Google Scholar
  9. 9.
    Maeda, S.: Probability measures on projections in von Neumann algebras, Rev. Math. Phys. 1 (1990), 235–290.Google Scholar
  10. 10.
    Wright, R.: The structure of projection-valued states: a generalization of Wigner's theorem, Int. J. Theor. Phys. 16 (1977), 567–573.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • P. Busch
    • 1
  1. 1.Department of MathematicsUniversity of HullHullU.K.

Personalised recommendations