## Algebraic methods in statistical mechanics and quantum field theory |

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abelian algebraic approach amenable arbitrary associated assumption automorphism Borel C*-algebra canonical commutation relations complete conclude consequence consider converges convex Corollary corresponding cyclic vector decomposition defined definition denote dense density matrix discussion Dixmier elements of 9 Emch evolution exists extended finite number Fock space furthermore G-abelianness G-invariant GNS construction Haag's theorem Hamiltonian hence Hilbert space Hilbert space 36 implies infinite invariant involutive irreducible representations isomorphism Jordan algebra Kadison Kastler KMS condition lemma linear manifold mapping mathematical mention norm normal notice observables obtained operators acting particular physical system physically equivalent postulates projector proof properties Proposition proved quantum field theory quasi-local remark representation of 9 representation tt respect restriction result satisfies Section Segal algebra self-adjoint elements self-adjoint operator semifinite separable sequence spectrum statistical mechanics Structure Axiom subsection subspace suppose symmetrized product symmetry group Theorem topology unique unitarily equivalent unitary operators