Tensor product of quaternion Hilbert modules

DOI10.1007/BF00046890zbMath0746.46047OpenAlexW2051591039MaRDI QIDQ1181249

Aharon Razon, Lawrence P. Horwitz

Publication date: 27 June 1992

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00046890

zbMATH Keywords

gauge transformationsgauge fieldsquaternion quantum mechanicstensor product of quaternion algebrasAnnihilation-creation operatorsquaternion scalar productstensor product of quaternion Hilbert modules

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Quantum field theory on lattices (81T25) Applications of functional analysis in quantum physics (46N50) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Finite-dimensional division rings (16K20) Tensor products in functional analysis (46M05)

Related Items

Category isomorphisms between Hilbert spaces over octonions and Hilbert spaces over Clifford algebras ⋮ Quantum mechanics: why complex Hilbert space? ⋮ Quaternionic quantum dynamics on complex Hilbert spaces ⋮ Uniqueness of the scalar product in the tensor product of quaternion Hilbert modules ⋮ The structure of symmetric tensor powers of composition algebras ⋮ Generalized quantum dynamics ⋮ A left linear weighted composition operator on quaternionic Fock space ⋮ Classification of left octonionic modules ⋮ Projection operators and states in the tensor product of quaternion Hilbert modules ⋮ On quaternionic functional analysis ⋮ Para-linearity as the nonassociative counterpart of linearity

Cites Work

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• Quaternion quantum mechanics: Second quantization and gauge fields
• Quaternionic quantum field theory
• Hilbert space with non-associative scalars. II
• Hilbert space with non-associative scalars. I
• The logic of quantum mechanics
• Exceptional gauge groups and quantum theory
• Composite systems in quaternionic quantum mechanics
• Quaternionic Hilbert space and colour confinement: I
• Principle of General Q Covariance
• ON A HILBERT SPACE WITH NONASSOCIATIVE SCALARS

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