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On the Hermitian projective line as a home for the geometry of quantum theory. (English) Zbl 1167.81394

Kielanowski, Piotr (ed.) et al., Geometric methods in physics. Proceedings of the xxvii workshop on geometric methods in physics, Białowieża, Poland, 29 June – 5 July 2008. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0610-0/hbk). AIP Conference Proceedings 1079, 14-25 (2008).
Summary: In the paper [the author, Int. J. Theor. Phys. 47, No. 10, 2754–2782 (2008; Zbl 1160.81398)], 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 \(\mathbb A\) and with Jordan-Lie and Lie-Jordan algebras. The associated geometries are (Hermitian) projective lines over \(\mathbb A\); their axiomatic definition and theory will be given in subsequent work [the author and M. Kinyon, in preparation].
For the entire collection see [Zbl 1157.81001].

MSC:

17C37 Associated geometries of Jordan algebras
51P05 Classical or axiomatic geometry and physics
81P05 General and philosophical questions in quantum theory

Citations:

Zbl 1160.81398
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