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

Abstract

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.

arXiv comment4 pages

References in corpus (2)

• Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics
• An alternative proof of Wigner theorem on quantum transformations based on elementary complex analysis

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