Quantum mechanics of the quaternionic Hilbert spaces based upon the imprimivity theorem

DOI10.1016/0034-4877(85)90017-5zbMath0587.46061OpenAlexW2012547456MaRDI QIDQ1072072

Piero Truini, Gianni Cassinelli

Publication date: 1985

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0034-4877(85)90017-5

zbMATH Keywords

time reversalimprimitivity theoremrealization of quantum mechanics in quaternionic Hilbert spacesthere exists a unique unitary skew-adjoint operator which commutes with all the observables

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Miscellaneous applications of functional analysis (46N99)

Related Items

Coherent states on quaternion slices and a measurable field of Hilbert spaces ⋮ Quantum mechanics: why complex Hilbert space? ⋮ Slice regular semigroups ⋮ Bibliography on quantum logics and related structures ⋮ On quaternionic functional analysis ⋮ CONTINUOUS SLICE FUNCTIONAL CALCULUS IN QUATERNIONIC HILBERT SPACES ⋮ Demicompactness results and Frobenuis Schur's decomposition for block operator matrices in right quaternionic Hilbert spaces

Cites Work

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• Positive Definite Measures
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• On Induced Representations of Groups
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