Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry

DOI10.1142/S0129055X17500210zbMath1372.81011arXiv1611.09029MaRDI QIDQ5348819

Valter Moretti, Marco Oppio

Publication date: 21 August 2017

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

Full work available at URL: https://arxiv.org/abs/1611.09029

zbMATH Keywords

representation theorylattice theoryvon Neumann algebrasquaternionic quantum mechanicsPoincaré groupreal quantum mechanicsreal spectral analysis

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) General theory of von Neumann algebras (46L10) General spectral theory of ordinary differential operators (34L05) Groups and semigroups of linear operators (47D03) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Special relativity (83A05) Applications of functional analysis in quantum physics (46N50) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Linear operators in (C^*)- or von Neumann algebras (47C15)

Related Items (9)

On the equivalence of complex and quaternionic quantum mechanics ⋮ Renormalized von Neumann entropy with application to entanglement in genuine infinite dimensional systems ⋮ On the invertibility of solutions of first order linear homogeneous differential equations in Banach algebras ⋮ The classification of rebit quantum channels ⋮ Quaternionic quantum mechanics in real Hilbert space ⋮ Antiunitary representations and modular theory ⋮ The correct formulation of Gleason's theorem in quaternionic Hilbert spaces ⋮ Quantum theory in quaternionic Hilbert space: How Poincaré symmetry reduces the theory to the standard complex one ⋮ Quaternionic quantum theory admits universal dynamics only for two-level systems

Cites Work

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• Spectral representations of normal operators in quaternionic Hilbert spaces via intertwining quaternionic PVMs
• Antiunitary representations and modular theory
• Orthomodularity in infinite dimensions; a theorem of M. Solèr
• Absolute-Valued Algebras
• The Connectedness of the Orthogonal Group in Hilbert Space
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