Skip to main content
SpringerLink
Log in

Classes of operations in quantum theory

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

Recent work of Davies and Lewis has shown how partially ordered vector spaces provide a setting in which the operational approach to statistical physical systems may be studied. In this paper, certain physically relevant classes of operations are identified in the abstract framework, some of their properties are derived and applications to the Von Neumann algebra model for quantum theory are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alfsen, E. M., Anderson, T. B.: Split faces of compact convex sets (pre-print).

  2. Cunningham, F.:L-structure inL-spaces. Trans. Am. Math. Soc.95, 274–299 (1960).

    Google Scholar 

  3. Davies, E. B.: Quantum stochastic processes. Commun. Math. Phys.15, 277–304 (1969).

    Google Scholar 

  4. ——, Lewis, J. T.: An operational approach to quantum probability. Commun. Math. Phys.17, 239–260 (1970).

    Google Scholar 

  5. Dixmier, J.: LesC*-algèbres et leurs representations. Paris: Gauthier-Villars 1964.

    Google Scholar 

  6. —— Les algèbres d'operateurs dans l'espace hilbertien. Paris: Gauthier-Villars 1969.

    Google Scholar 

  7. Edwards, C. M.: The operational approach to algebraic quantum theory I. Commun. Math. Phys.16, 207–230 (1970).

    Google Scholar 

  8. Edwards, C. M., Gerzon, M. A.: Monotone convergence in partially ordered vector spaces. Ann. Inst. Henri Poincaré A12, 323–328 (1970).

    Google Scholar 

  9. Effros, E. G.: Order ideals in aC*-algebra and its dual. Duke Math. J.30, 391–412 (1963).

    Google Scholar 

  10. Ellis, A. J.: The duality of partially ordered normed vector spaces. J. London Math. Soc.39, 730–744 (1964).

    Google Scholar 

  11. —— Linear operators in partially ordered vector spaces. J. London Math. Soc.41, 323–332 (1966).

    Google Scholar 

  12. Gerzon, M. A.: Split faces of convex sets (in preparation).

  13. Haag, R., Kastler, D.: An algebraic approach to quantum field theory. J. Math. Phys.5, 846–861 (1964).

    Google Scholar 

  14. Hellwig, K.-E., Kraus, K.: Pure operations and measurements. Commun. Math. Phys.11, 214–220 (1969).

    Google Scholar 

  15. —— —— Operations and measurements II. Commun. Math. Phys.16, 142–147 (1970).

    Google Scholar 

  16. Kadison, R. V.: Isometries of operator algebras. Ann. Math.54, 325–338 (1950).

    Google Scholar 

  17. Mackey, G. W.: Mathematical foundations of quantum mechanics. New York: Benjamin 1963.

    Google Scholar 

  18. Prosser, R. T.: On the ideal structure of operator algebras. Mem. Am. Math. Soc.45 (1963).

  19. Segal, I. E.: Postulates for general quantum mechanics. Ann. Math.48, 930–948 (1948).

    Google Scholar 

  20. Stormer, E.: Positive linear maps of operator algebras. Acta Math.110, 233–278 (1963).

    Google Scholar 

  21. Von Neumann, J.: Mathematical foundations of quantum mechanics. Princeton: Princeton University Press 1957.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Queen's College, Oxford

    C. M. Edwards

Authors
  1. C. M. Edwards
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Edwards, C.M. Classes of operations in quantum theory. Commun.Math. Phys. 20, 26–56 (1971). https://doi.org/10.1007/BF01646732

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01646732

Keywords

Search

Navigation