Geometry of Jordan Structures and Quantum Mechanics

Wolfgang Bertram

Piero Truini, Lawrence C. Biedenharn

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.

Ricardo Alejandro Troncoso Perez, Cristian Andres Martinez Silva

José F. Cariñena, Alberto Ibort, G. Marmo +4 more

Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to quantum mechanics. We will concentrate our attention into quantum theories and we will show how to use in a systematic way the transition from algebraic to geometrical structures to explore their geometry, mainly its Jordan‐Lie structure.

James Thomas Wheeler

Paul Bracken