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The Classical Case
The Quantum Case
3 other sections not shown
A. S. Wightman algebra arbitrary atom axiom bijective Boolean CROC Borel sets c-ideal c-morphism canonical Chapter classical propositional system closed subspaces commutation complete lattice condition contains Conversely corresponding countable definite Hermitian form denote dimension direct union disintegration easy to verify ensemble equations exists family of Hilbert finite following theorem Foundations of Quantum function Galilean group Galilean particle Galilean transformations given Hamiltonian Hermitian form Hilbert space ideal measurement identical imprimitivity systems induced irreducible propositional system irreducible representation isomorphic lemma let us show linear variety mapping Math Mathematical maximal element Neumann density operator notion obtained orthocomplementation orthocomplemented orthogonal particular phase factor physical system probability projective geometry projectors Proof properties prove Quantum Mechanics quantum physics realized relation satisfies Section self-adjoint operator semilinear transformation space H spin sub-CROC sublattice subset tion topology tribe trivial true unitary vector space weak modularity whence