On the Hermitian projective line as a home for the geometry of Quantum Theory

Details On the Hermitian projective line as a home for the geometry of Quantum Theory On the Hermitian projective line as a home for the geometry of Quantum Theory

2008-09-03

arxiv.org/abs/0809.0561v1

Physics

Mathematical Physics

submitted to Proceedings of XXVII Workshop on Geometrical Methods in Physics, Bialowieza 2008

Scientific paper

10.1063/1.3043855

In the paper "Is there a Jordan geometry underlying quantum physics?" (Int. J. Theor. Phys., to appear; arXiv:0801.3069 [math-ph]), 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, and with Jordan-Lie and Lie-Jordan algebas. The associated geometries are (Hermitian) projective lines over an associative algebra; their axiomatic definition and theory will be given in subsequent work with M. Kinyon.

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