An ℰ6⊗𝒰(1) invariant quantum mechanics for a Jordan pair
- 1 July 1982
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 23 (7) , 1327-1345
- https://doi.org/10.1063/1.525496
Abstract
Quantum mechanical spaces associated with geometries based on exceptional groups are of interest as models for internal (quark) symmetries. Using the concept of a Jordan pair, two copies of complex 3×3 octonionic Jordan algebras (ℳ83) are shown to define a quantum mechanics over the complex octonionic plane having ℰ6⊗𝒰(1) as automorphism group. The unusual features of this new quantal structure (neither a projective geometry, nor a lattice) are discussed.Keywords
This publication has 15 references indexed in Scilit:
- Moufang plane and octonionic Quantum MechanicsCommunications in Mathematical Physics, 1978
- Jordan algebras and their applicationsBulletin of the American Mathematical Society, 1978
- Exceptional Lie Algebras and Related Algebraic and Geometric StructuresBulletin of the London Mathematical Society, 1977
- On the geometry of inner idealsJournal of Algebra, 1973
- Quadratic Jordan algebras and cubing operationsTransactions of the American Mathematical Society, 1971
- The Freudenthal-Springer-Tits constructions of exceptional Jordan algebrasTransactions of the American Mathematical Society, 1969
- Imbedding of Jordan Algebras into Lie Algebras. IAmerican Journal of Mathematics, 1967
- A GENERAL THEORY OF JORDAN RINGSProceedings of the National Academy of Sciences, 1966
- Characterization of a Class of Cubic FormsIndagationes Mathematicae, 1962
- On an Algebraic Generalization of the Quantum Mechanical FormalismAnnals of Mathematics, 1934