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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bargmann, V.: Notes on Wigner's theorem on symmetry operations, J. Math. Phys. 5 (1964), 862–868.
Busch, P.: Quantum extensions of quantum statistical models, Preprint, 1998.
Busch, P. and Quadt, R.: Operational characterization of irreversibility, Report Series, Department of Mathematics, University of Hull, 1998.
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.
Davies, E. B.: Quantum Theory of Open Systems, Academic Press, New York, 1976.
Emch, G. G.: Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley, New York, 1972.
Kadison, R. V.: Transformations of states in operator theory and dynamics, Topology 3(Suppl. 2) (1965), 177–198.
Kadison, R. V.: Isometries of operator algebras, Ann. of Math. 54 (1951), 325–338.
Maeda, S.: Probability measures on projections in von Neumann algebras, Rev. Math. Phys. 1 (1990), 235–290.
Wright, R.: The structure of projection-valued states: a generalization of Wigner's theorem, Int. J. Theor. Phys. 16 (1977), 567–573.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Busch, P. Stochastic Isometries in Quantum Mechanics. Mathematical Physics, Analysis and Geometry 2, 83–106 (1999). https://doi.org/10.1023/A:1009822315406
Issue Date:
DOI: https://doi.org/10.1023/A:1009822315406