QUASIBOOLEAN ALGEBRAS AND SIMULTANEOUSLY DEFINITE PROPERTIES IN QUANTUM-MECHANICS

Citation
Jl. Bell et Rk. Clifton, QUASIBOOLEAN ALGEBRAS AND SIMULTANEOUSLY DEFINITE PROPERTIES IN QUANTUM-MECHANICS, International journal of theoretical physics, 34(12), 1995, pp. 2409-2421
Citations number
12
Categorie Soggetti
Physics
ISSN journal
00207748
Volume
34
Issue
12
Year of publication
1995
Pages
2409 - 2421
Database
ISI
SICI code
0020-7748(1995)34:12<2409:QAASDP>2.0.ZU;2-H
Abstract
We define and characterize a new abstract notion of ''quasiBoolean alg ebra,'' intermediate in nature between an (ortho)lattice and a Boolean algebra. It will turn out that such algebras are natural candidates f or representing the simultaneously definite properties of a quantum sy stem. We then prove a general theorem about maximal quasiBoolean subal gebras of an ortholattice which we use to derive a number of different proposals in the literature for what properties of a quantum system s hould be regarded as simultaneously definite.