Abstract
Uniformities describing the distinguishability of states and of observables are discussed in the context of general statistical theories and are shown to be related to distinguished subspaces of continuous observables and states, respectively. The usual formalism of quantum mechanics contains no such physical uniformity for states. Using recently developed tools of quantum harmonic analysis, a natural one-to-one correspondence between continuous subspaces of nonrelativistic quantum and classical mechanics is established, thus exhibiting a close interrelation between physical uniformities for quantum states and compactifications of phase space. General properties of the completions of the quantum state space with respect to these uniformities are discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Ludwig, “Imprecision in Physics,” inStructure and Approximation in Physical Theories, A. Hartkämper and H.-J. Schmidt, eds. (Plenum, New York, 1981).
G. Ludwig,Foundations of Quantum Mechanics (Springer, New York, 1983).
H. Neumann,Found. Phys.,13, 761 (1983).
R. Werner,The Concept of Embeddings in Statistical Mechanics, Doctoral Dissertation, Marburg, 1982.
R. Haag and D. Kastler,J. Math. Phys.,5, 848 (1964).
N. Bourbaki,General Topology, Part 1 (Hermann, Paris, 1966).
R. Nagel, “Order Unit and Base Norm Spaces,” inFoundations of Quantum Mechanics and Ordered Linear Spaces (Lecture Notes in Physics 29), A. Hartkämper and H. Neumann, eds. (Springer, New York, 1974).
Y. Wong and K. Ng.Partially Ordered Topological Vector Spaces (Clarendon Press, Oxford, 1973).
H. H. Schaefer,Topological Vector Spaces (Springer, New York, 1971).
R. E. Chandler,Hausdorff Compactifications (Dekker, New York, 1976).
J. Dugundji,Topology (Allyn and Bacon, Boston, 1966).
R. Werner, “Quantum Harmonic Analysis on Phase Space,” Preprint, Osnabrück, 1982.
Y. Katznelson,An Introduction to Harmonic Analysis (Wiley, New York, 1968).
R. G. Douglas,C*-Algebra Extensions and K-Homology (Princeton U.P., Princeton, 1980).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Werner, R. Physical uniformities on the state space of nonrelativisitic quantum mechanics. Found Phys 13, 859–881 (1983). https://doi.org/10.1007/BF01906273
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01906273