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


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.


Hilbert Space Quantum Mechanic Symmetry Transformation Classical Theorem Principal Angle 
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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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