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An elementary proof for the non-bijective version of Wigner's theorem

Gehér, G. P. (2014) An elementary proof for the non-bijective version of Wigner's theorem. Physics Letters A, 378 (30-31). pp. 2054-2057. ISSN 0375-9601

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To link to this item DOI: 10.1016/j.physleta.2014.05.039

Abstract/Summary

The non-bijective version of Wigner’s theorem states that a map which is defined on the set of self-adjoint, rank-one projections (or pure states) of a complex Hilbert space and which preserves the transition probability between any two elements, is induced by a linear or antilinear isometry. We present a completely new, elementary and very short proof of this famous theorem which is very important in quantum mechanics. We do not assume bijectivity of the mapping or separability of the underlying space like in many other proofs.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:81505
Publisher:Elsevier

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