Division algebras and quantum theory

DOI10.1007/s10701-011-9566-zzbMath1259.81023arXiv1101.5690OpenAlexW2000372033WikidataQ62443363 ScholiaQ62443363MaRDI QIDQ1929299

John C. Baez

Publication date: 7 January 2013

Published in: Foundations of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.5690

zbMATH Keywords

quantum theorydualityconvex conegroup representationJordan algebraquaternionoctoniondivision algebra

Mathematics Subject Classification ID

Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces (54F05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Applications of group representations to physics and other areas of science (20C35) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (16)

The operational foundations of PT-symmetric and quasi-Hermitian quantum theory ⋮ A Quantum Information-Based Refoundation of Color Perception Concepts ⋮ Quantum mechanics: why complex Hilbert space? ⋮ Some Nearly Quantum Theories ⋮ Special Vinberg cones, invariant admissible cubics and special real manifolds ⋮ Tensor- and spinor-valued random fields with applications to continuum physics and cosmology ⋮ Geometry of color perception. II: Perceived colors from real quantum states and Hering's rebit ⋮ Dynamical States and the Conventionality of (Non-) Classicality ⋮ The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer ⋮ The relativity of color perception ⋮ From Riemannian trichromacy to quantum color opponency via hyperbolicity ⋮ Octonions, exceptional Jordan algebra and the role of the group \(F_4\) in particle physics ⋮ Special Vinberg cones ⋮ Quaternionic quantum theory admits universal dynamics only for two-level systems ⋮ General quantum theory—unification of classical and modal quantum theories ⋮ Hunt's colorimetric effect from a quantum measurement viewpoint

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