English

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

Mathematical Physics 2009-11-13 v1 math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.0809.0561,
  title  = {On the Hermitian projective line as a home for the geometry of Quantum Theory},
  author = {Wolfgang Bertram},
  journal= {arXiv preprint arXiv:0809.0561},
  year   = {2009}
}

Comments

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