On the Hermitian Projective Line as a Home for the Geometry of Quantum Theory

Journal Article · Tue Nov 18 00:00:00 EST 2008 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3043855· OSTI ID:21254869

Bertram, Wolfgang ^[1]

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1. Institut Elie Carton Nancy, Nancy-Universite, CNRS, INRIA, Boulevard des Aiguillettes, B.P. 239, F-54506 Vandoeuvre-les-Nancy (France)

In the paper [1], generalized projective geometries have been proposed as a framework for a geometric formulation of Quantum Theory. In the present note, we refine this proposition by discussing further structural features of Quantum Theory: the link with associative involutive algebras A and with Jordan-Lie and Lie-Jordan algebas. The associated geometries are (Hermitian) projective lines over A; their axiomatic definition and theory will be given in subsequent work with M. Kinyon [2].

• OSTI ID: 21254869
• Journal Information: AIP Conference Proceedings, Vol. 1079, Issue 1; Conference: 27. workshop on geometric methods in physics, Bialowieza (Poland), 29 Jun - 5 Jul 2008; Other Information: DOI: 10.1063/1.3043855; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
AXIOMATIC FIELD THEORY
GEOMETRY
LIE GROUPS
NUMERICAL ANALYSIS