Moufang plane and octonionic quantum mechanics

DOI10.1007/BF01609468zbMath0409.22018MaRDI QIDQ1258839

C. Piron, Henri Ruegg, Murat Gunaydin

Publication date: 1978

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

zbMATH Keywords

Jordan AlgebraAutomorphism Group of the Moufang PlaneAxioms of Quantum MechanicsExceptional Real Lie GroupNondesarguian Projective PlaneProbability Function Satisfying Gleason's Axioms

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Exceptional Jordan structures (17C40) Applications of Lie groups to the sciences; explicit representations (22E70) Lie algebras of Lie groups (22E60) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Non-Desarguesian affine and projective planes (51A35) Other nonassociative rings and algebras (17D99)

Related Items (41)

Quaternionic quantum field theory ⋮ Scalar manifolds and Jordan pairs in supergravity ⋮ Super Yang-Mills, division algebras and triality ⋮ Geometrical applications of split octonions ⋮ ORBITS OF EXCEPTIONAL GROUPS, DUALITY AND BPS STATES IN STRING THEORY ⋮ The octonions ⋮ Freudenthal gauge theory ⋮ \(S^ 7\) and \({\widehat {S^ 7}}\) ⋮ Exceptional quantum geometry and particle physics ⋮ Three graded exceptional algebras and symmetric spaces ⋮ Octonion-valued forms and the canonical 8-form on Riemannian manifolds with a Spin(9)-structure ⋮ Exceptional gauge groups and quantum theory ⋮ Spectrum generating conformal and quasiconformal U-duality groups, supergravity and spherical vectors ⋮ On an exceptional nonassociative superspace ⋮ Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra ⋮ Rotations in the space of Split octonions ⋮ Orbits and attractors for \(N=2\) Maxwell-Einstein supergravity theories in five dimensions ⋮ A construction relating Clifford algebras and Cayley–Dickson algebras ⋮ The quasi-nonassociative exceptional F(4) deformed quantum oscillator ⋮ Exceptional quantum geometry and particle physics. II ⋮ A general theory of quantum relativity ⋮ \(\mathbb{R} \otimes \mathbb{C}\otimes \mathbb{H}\otimes \mathbb{O}\)-valued gravity as a grand unified field theory ⋮ Differential calculus on Jordan algebras and Jordan modules ⋮ \(\mathcal N = 8\) non-BPS attractors, fixed scalars and magic supergravities ⋮ Monopole star products are non-alternative ⋮ States in non-associative quantum mechanics: uncertainty relations and semiclassical evolution ⋮ On the moduli space of non-BPS attractors for \(\mathcal N=2\) symmetric manifolds ⋮ Non-representable hyperbolic matroids ⋮ Degeneration of groups of type \(E_7\) and minimal coupling in supergravity ⋮ Exceptional Jordan matrix models, octonionic strings/branes and star product deformations ⋮ Octonions, exceptional Jordan algebra and the role of the group \(F_4\) in particle physics ⋮ Unnamed Item ⋮ Nonassociativity, Malcev algebras and string theory ⋮ Quaternion gauge fields. Pseudocolor ⋮ Quaternion quantum mechanics: Second quantization and gauge fields ⋮ Wrapped Branes as Qubits ⋮ A theorem about states on quantum logics. States on Jordan algebras ⋮ Nambu quantum mechanics: a nonlinear generalization of geometric quantum mechanics ⋮ The Jordan pair content of the magic square and the geometry of the scalars in \(N=2\) supergravity ⋮ Complexification of the exceptional Jordan algebra and its application to particle physics ⋮ An ℰ6⊗𝒰(1) invariant quantum mechanics for a Jordan pair

Cites Work

• Alternativkörper und der Satz vom vollständigen Vierseit \((D_9)\)
• On an algebraic generalization of the quantum mechanical formalism
• Lie groups in the foundations of geometry
• Über eine nicht-desarguessche ebene projektive Geometrie
• Quark structure and octonions
• ON A HILBERT SPACE WITH NONASSOCIATIVE SCALARS
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