Skip to main content
SpringerLink
Log in

Algebra and Geometry in the Theory of Mixed States

  • Chapter
Symmetries in Science V

  • 211 Accesses

Abstract

It is my intention to show some aspects of the very the rich theory of mixed states. A more or less subjective selection of the topics for this purpose was necessary. A certain complement to this selection is reviewed in1.2.3.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Fano, U., Rev. Mod. Phys. 29 (1957) 74

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Wehrl, A., Rev. Mod. Phys. 50 (1978) 221

    Article  MathSciNet  ADS  Google Scholar 

  3. Bluhm, K.: Density Matrix Theory and Applications., Plenum Press, New York, 1981

    Book  Google Scholar 

  4. Berry, M. V. Proc. Royal. Soc. Lond. A 392 (1984) 45

    Article  ADS  MATH  Google Scholar 

  5. Simon, B., Phys. Rev. Lett. 51 (1983) 2167

    Article  MathSciNet  ADS  Google Scholar 

  6. Born, M., Z. Phys. 40 (1926) 167

    ADS  MATH  Google Scholar 

  7. Born, M. and Fock, V., Z. Phys. 51 (1928) 165

    Article  ADS  MATH  Google Scholar 

  8. Born, M. and Oppenheimer, J., Ann. d. Phys. 84 (1927) 457

    Article  ADS  MATH  Google Scholar 

  9. Aharonow, Y., Anandan, J., Phys. Rev. Lett. 58 (1987) 1593

    Article  MathSciNet  ADS  Google Scholar 

  10. Littlejohn, R.G., Phys. Rev. Lett. 61 (1988) 2159

    Article  MathSciNet  ADS  Google Scholar 

  11. Uhlmann, A., Annalen d. Phys. 46 (1989) 63

    Article  MathSciNet  ADS  Google Scholar 

  12. Berry, M., Quantum Adiabatic Holonomy. In: Anomalies, phases, defects (ed. M. Bregola, G. Marmo, G. Morandi), Bibliopolis, Naples, 1990

    Google Scholar 

  13. Geometric Phases in Physics. (ed. A.Shapere, F.Wilczek), World Scientific Publishing Co., Singapure, 1990

    Google Scholar 

  14. Akemann, C.A., Pedersen, G.K., Facial Structure in Operator Algebra Theory. Preprint, Kopenhavns, June 1990.

    Google Scholar 

  15. Uhlmann, A., Rep. Math. Phys. 7 (1975) 449

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Uhlmann, A., Rep. Math. Phys. 9 (1976) 273

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Raggio, G. A., Lett. Math. Phys. 6 (1982) 233

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Araki, H. and Raggio, G. A., Lett. Math. Phys. 6 (1982) 237

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Alberti, P. M., Lett. Math. Phys. 7 (1983) 25

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Alberti, P. M. and Uhlmann, A., Lett. Math. Phys. 7 (1983) 107

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Cantoni, V., Comm. Math. Phys. 44 (1975) 125

    Article  MathSciNet  ADS  Google Scholar 

  22. Uhlmann, A., Ann. d. Physik 42 (1985) 524

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. Uhlmann, A., Rep. Math. Phys. 24 (1986) 229

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Uhlmann, A., Parallel Transport and Holonomy along Density Operators. In: “Differential Geometric Methods in Theoretical Physics” (ed. H.D. Doebner, J.D. Hennig), World Sci. Publ., Singapore 1987, p. 246–254

    Google Scholar 

  25. Bures, D. J. C., Trans. Amer. Math. Soc. 135 (1969) 199

    MathSciNet  MATH  Google Scholar 

  26. Fock, V., Z. Phys. 49 (1928) 323

    Article  ADS  MATH  Google Scholar 

  27. Wilczek, F. and Zee, A., Phys. Rev. Lett. 52 (1984) 2111

    Article  MathSciNet  ADS  Google Scholar 

  28. Dabrowski, L., Grosse, H., On Quantum Holonomy for Mixed States. Preprint, Wien, U W ThP h-1988–36

    Google Scholar 

  29. Dabrowski, L., Jadcyk, A., Quantum Statistical Holonomy. Preprint, Trieste, 155/88/FM

    Google Scholar 

  30. Dabrowski, L. A Superposition Principle for Mixed States? Preprint, Trieste, 156/88/FM

    Google Scholar 

  31. Uhlmann, A., Gauge Field Governing Parallel Transport along Mixed States. Preprint, Wien, UWThPh-1990–25

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Leipzig, Leipzig, Germany

    Armin Uhlmann

Authors
  1. Armin Uhlmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Southern Illinois University, Carbondale, Illinois, USA

    Bruno Gruber

  2. Duke University, Durham, North Carolina, USA

    L. C. Biedenharn

  3. Technical University, Clausthal, Germany

    H. D. Doebner

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Uhlmann, A. (1991). Algebra and Geometry in the Theory of Mixed States. In: Gruber, B., Biedenharn, L.C., Doebner, H.D. (eds) Symmetries in Science V. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3696-3_27

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-3696-3_27

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6643-0

  • Online ISBN: 978-1-4615-3696-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation