Classical systems and observables in quantum mechanics

Generalized quantum mechanics

“…It explores the convex structures of quantum mechanics with a special attention concentrated on the convex set of all states (pure and mixed) of a quantum system. The description of quantum mechanics from that point of view was most systematically explored by Ludwig [14] and further developed in [3][4][5][6]11,[15][16][17]19,21,22]; it now becomes one of main currents in the foundation of quantum theory. The synthesis of the convex and the algebraic approaches has been gradually achieved [3,5,6,[9][10][11]16,19].…”

A new physical characterisation of classical systems in quantum mechanics

“…Then every element Of RMo is a disjoint union of 'monomials" ~r a = n pxi-l(5-~, ~i E T. A vector-valued measure is defined on RMu if it is i=1 defined on these monomials. We put A u = RMo and define x fora E RMv,X EMu, × is a vectorvalued measure on RMo such that X(RMu) = My (compare also the proof of Theorem 8 (Neumann, 1971)). This completes the proof of the theorem.…”

“…On the other hand the connection between observables and the description of classical systems allows us to carry over results valid for classical systems to regions of quantum mechanical systems (Neumann, 1971).…”

Generalized Quantum Mechanics

“…It explores the convex structures of quantum mechanics with a special attention concentrated on the convex set of all states (pure and mixed) of a quantum system. The description of quantum mechanics from that point of view was most systematically explored by Ludwig [14] and further developed in [3][4][5][6]11,[15][16][17]19,21,22]; it now becomes one of main currents in the foundation of quantum theory. The synthesis of the convex and the algebraic approaches has been gradually achieved [3,5,6,[9][10][11]16,19].…”