Description:
<jats:p>The algebraic formulation of quantum statistical mechanics is extended so as to include local unbounded observables. We start, in a usual way, with a C*-algebra U of quasilocal bounded observables in Fock space HF, an arbitrary, locally normal state φ on U, and a corresponding Gel'fand-Naimark-Segal (GNS) representation Rφ of U in a Hilbert space Hφ. We then construct a set QL of local, closed operators whose domains are dense in HF, such that QL includes all the local observables of the system. The representation Rφ is then extended so as to provide a *-homomorphism of HL into the closed, densely defined operators in Hφ. Correspondingly, a number of results previously established for the local bounded observables are extended to the unbounded ones. For appropriate classes of locally normal states, these extended results include the Kubo-Martin-Schwinger boundary conditions, the spatially asymptotic and ergodic properties of space-correlation functions, and the temporally ergodic properties of time-correlation functions. It is also shown that, for locally normal Gibbs states, the time correlations between elements of a specified subset of QL are thermodynamical limits of the corresponding correlations for finite systems.</jats:p>