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The structure of projection-valued states: A generalization of Wigner's theorem

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Abstract

A projection-valued state is defined to be a completely orthoadditive map from the projections on one Hilbert space into the projections on another Hilbert space, which preserves the unit. Any such mapping is shown to have the formP →U 1(P ⊗ 11)U −11 ⊕U 2(P ⊗ 12)U −12 , whereU 1 is unitary andU 2 is antiunitary, generalizing Wigner's theorem on symmetry transformations. A physical interpretation is given and the relation to “quantum logic” is discussed.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, 01003, Amherst, Massachusetts

    Ron Wright

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  1. Ron Wright
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The contents of this paper are a portion of the author's dissertation at the University of Massachusetts at Amherst.

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Wright, R. The structure of projection-valued states: A generalization of Wigner's theorem. Int J Theor Phys 16, 567–573 (1977). https://doi.org/10.1007/BF01811089

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  • DOI: https://doi.org/10.1007/BF01811089

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