Generalized symmetry transformations on quaternionic indefinite inner product spaces: An extension of quaternionic version of Wigner's theorem

DOI10.1007/s00220-003-0957-7zbMath1053.46012OpenAlexW2093797035MaRDI QIDQ1423654

Peter Šemrl

Publication date: 7 March 2004

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-003-0957-7

zbMATH Keywords

indefinite inner productsWigner's theoremquaternionic Hilbert spaces

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Linear operators on spaces with an indefinite metric (47B50)

Related Items (14)

Maps on matrix spaces ⋮ Maps on states preserving generalized entropy of convex combinations ⋮ Wigner's theorem on Grassmann spaces ⋮ Characterization of orthomaps on the Cayley plane ⋮ Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics ⋮ Wigner-type theorem on transition probability preserving maps in semifinite factors ⋮ Zero product preserving maps on matrix rings over division rings ⋮ Alternative descriptions in quaternionic quantum mechanics ⋮ Maps on idempotent matrices over division rings ⋮ Hua's fundamental theorem of geometry of rectangular matrices over EAS division rings ⋮ Transition probability preserving maps on a Grassmann space in a semifinite factor ⋮ Preservers of generalized orthogonality on finite dimensional real vector and projective spaces ⋮ Unnamed Item ⋮ A variant of Wigner's functional equation

Cites Work

• Unnamed Item
• Symmetry transformations in indefinite metric spaces. A generalization of Wigner's theorem
• Wigner's theorem on symmetries in indefinite metric spaces
• Orthogonality preserving transformations on indefinite inner product spaces: Generalization of Uhlhorn's version of Wigner's theorem
• Applying projective geometry to transformations on rank one idempotents
• Generalization of Wigner's unitary-antiunitary theorem for indefinite inner product spaces
• Automorphisms of the poset of skew projections
• Additive isometries on a quaternionic Hilbert space
• Note on Wigner's Theorem on Symmetry Operations

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