Hilbert Lattice Equations

Details Hilbert Lattice Equations Hilbert Lattice Equations

2009-12-08

arxiv.org/abs/0912.1461v2

Annales Henri Poincare, 10, 1335-1358 (2010)

Physics

Mathematical Physics

24 pages, 3 figures

Scientific paper

10.1007/s00023-009-0019-6

There are five known classes of lattice equations that hold in every infinite dimensional Hilbert space underlying quantum systems: generalised orthoarguesian, Mayet's E_A, Godowski, Mayet-Godowski, and Mayet's E equations. We obtain a result which opens a possibility that the first two classes coincide. We devise new algorithms to generate Mayet-Godowski equations that allow us to prove that the fourth class properly includes the third. An open problem related to the last class is answered. Finally, we show some new results on the Godowski lattices characterising the third class of equations.

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