A direct proof of Wigner's theorem on maps which preserve transition probabilities between pure states of quantum systems

DOI10.1016/0003-4916(90)90213-8zbMath0875.46008OpenAlexW2005167555MaRDI QIDQ1816254

D. F. Almeida, Chandra Shekhar Sharma

Publication date: 8 April 1997

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0003-4916(90)90213-8

zbMATH Keywords

unitary operatortransition probabilitycomplex Hilbert spaceWigner's theorem

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Applications of operator theory in the physical sciences (47N50) Applications of functional analysis in quantum physics (46N50)

Related Items (21)

A new proof of Wigner's theorem ⋮ Min-phase-isometries and Wigner's theorem on real normed spaces ⋮ Additive isometries on a quaternionic Hilbert space ⋮ On Wigner's theorem: Remarks, complements, comments, and corollaries ⋮ Isometry and phase-isometry of non-Archimedean normed spaces ⋮ MIN-PHASE-ISOMETRIES IN STRICTLY CONVEX NORMED SPACES ⋮ WIGNER’S THEOREM IN -TYPE SPACES ⋮ Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics ⋮ On Wigner's theorem in smooth normed spaces ⋮ On the Aleksandrov Problem of Conservative Distances ⋮ Local automorphisms of the sets of states and effects on a Hilbert space ⋮ Entanglement-saving channels ⋮ An elementary proof for the non-bijective version of Wigner's theorem ⋮ Maps on classes of Hilbert space operators preserving measure of commutativity ⋮ Phase-isometries on real normed spaces ⋮ Representation of symmetry transformations on the sets of tripotents of spin and Cartan factors ⋮ On normed spaces with the Wigner property ⋮ Wigner's theorem on the Tsirelson space \(T\) ⋮ A generalization of Wigner’s unitary–antiunitary theorem to Hilbert modules ⋮ A note on Tingley’s problem and Wigner’s theorem in the unit sphere of ^∞(Γ)-type spaces ⋮ A variant of Wigner's functional equation

Cites Work

• Calculus on complex Banach spaces
• A new differential calculus on a complex Banach space with application to variational problems of quantum theory
• Spectral theory for unitary operators on a quaternionic Hilbert space
• Phenomenological Distinction between Unitary and Antiunitary Symmetry Operators
• Semilinear operators
• Additive functionals and operators on a quaternionic Hilbert space
• Note on Wigner's Theorem on Symmetry Operations
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