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Communications in Mathematical Physics

, Volume 217, Issue 2, pp 409–421 | Cite as

Transformations on the Set of All n-Dimensional Subspaces of a Hilbert Space Preserving Principal Angles

  • Lajos Molnár

Abstract:

Wigner's classical theorem on symmetry transformations plays a fundamental role in quantum mechanics. It can be formulated, for example, in the following way: Every bijective transformation on the set ℒ of all 1-dimensional subspaces of a Hilbert space H which preserves the angle between the elements of ℒ is induced by either a unitary or an antiunitary operator on H. The aim of this paper is to extend Wigner's result from the 1-dimensional case to the case of n-dimensional subspaces of H with n∈ℕ fixed.

Keywords

Hilbert Space Quantum Mechanic Symmetry Transformation Classical Theorem Principal Angle 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Lajos Molnár
    • 1
  1. 1.Institute of Mathematics and Informatics, University of Debrecen, 4010 Debrecen, P.O.Box 12, Hungary¶E-mail: molnarl@math.klte.huHU

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