Quantum theory in quaternionic Hilbert space: How Poincaré symmetry reduces the theory to the standard complex one

DOI10.1142/S0129055X19500132zbMath1471.81010arXiv1709.09246OpenAlexW2758775275MaRDI QIDQ5237787

Marco Oppio, Valter Moretti

Publication date: 18 October 2019

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

Full work available at URL: https://arxiv.org/abs/1709.09246

zbMATH Keywords

spectral theoryrepresentation theoryfoundation of quantum mechanicsquaternionic functional analysis

Mathematics Subject Classification ID

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) 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) Quaternionic functional analysis (46S05)

Related Items (3)

Order theoretical structures in atomic JBW-algebras: disjointness, bands, and centres ⋮ Slice-by-slice and global smoothness of slice regular and polyanalytic functions ⋮ Quaternionic quantum theory admits universal dynamics only for two-level systems

Cites Work

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• Antiunitary representations and modular theory
• Orthomodularity in infinite dimensions; a theorem of M. Solèr
• Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry
• Absolute-Valued Algebras
• The Connectedness of the Orthogonal Group in Hilbert Space
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