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International Journal of Theoretical Physics

, Volume 39, Issue 6, pp 1463–1466 | Cite as

Wigner-Type Theorem on Symmetry Transformations in Type II Factors

  • Lajos Molnár
Article

Abstract

Wigner's theorem on symmetry transformations can be formulated in the followingway. If φ is a bijective map on the set of all nonzero minimal projections in atype I factor A which preserves transition probabilities with respect to a faithfulnormal semifinite trace, then it can be extended to a linear *-automorphism orto a linear *-antiautomorphism of A. In this paper we prove a natural analogueof this statement for type II factors.

Keywords

Field Theory Elementary Particle Quantum Field Theory Symmetry Transformation Minimal Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

  1. 1.
    L. J. Bunce and D. M. Wright (1992). The Mackey-Gleason problem, Bull.Am.Math.Soc. 26, 288–293.Google Scholar
  2. 2.
    P. Civin and B. Yood (1965). Lie and Jordan structures in Banach algebras, Pacific J.Math. 15, 775–797.Google Scholar
  3. 3.
    I. N. Herstein (1956). Jordan homomorphisms, Trans.Am.Math.Soc. 81, 331–341.Google Scholar
  4. 4.
    R. V. Kadison and J. R. Ringrose (1986). Fundamentals of the Theory of Operator Algebras, Vol II, Academic Press.Google Scholar
  5. 5.
    L. Molnár (1997). The set of automorphisms of B(H) is topologically reflexive in B(B(H)), Studia Math. 122, 183–193.Google Scholar
  6. 6.
    L. Molnár (1999). A generalization of Wigner's unitary-antiunitary theorem to Hilbert modules, J.Math.Phys. 40, 5544–5554.Google Scholar
  7. 7.
    L. Molnár (2000). Generalization of Wigner's unitary-antiunitary theorem for indefinite inner product spaces, Commun.Math.Phys. 210, 785–791.Google Scholar
  8. 8.
    L. Molnár, A Wigner-type theorem on symmetry transformations in Banach spaces, submitted.Google Scholar
  9. 9.
    E. Størmer (1965). On the Jordan structure of C*-algebras, Trans.Am.Math.Soc. 120, 438–447.Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Lajos Molnár
    • 1
  1. 1.Institute of MathematicsLajos Kossuth UniversityDebrecenHungary

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