Quantum Logic and Non-Commutative Geometry

Details Quantum Logic and Non-Commutative Geometry Quantum Logic and Non-Commutative Geometry

2004-05-26

arxiv.org/abs/quant-ph/0405159v1

Int.J.Theor.Phys. 46 (2007) 49-62

Physics

Quantum Physics

16 pages, to be published in the International Journal of Theoretical Physics, without Appendix

Scientific paper

We propose a general scheme for the "logic" of elementary propositions of physical systems, encompassing both classical and quantum cases, in the framework given by Non Commutative Geometry. It involves Baire*-algebras, the non-commutative version of measurable functions, arising as envelope of the C*-algebras identifying the topology of the (non-commutative) phase space. We outline some consequences of this proposal in different physical systems. This approach in particular avoids some problematic features appearing in the definition of the state of "initial conditions" in the standard W*-algebraic approach to classical systems.

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