Spectral stochastic processes arising in quantum mechanical models with a non-L2 ground state

Details Spectral stochastic processes arising in quantum mechanical models with a non-L2 ground state Spectral stochastic processes arising in quantum mechanical models with a non-L2 ground state

1994-10-12

arxiv.org/abs/hep-th/9410083v1

Lett. Math. Phys. 35 (1995) 251-262

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, Plain Tex

Scientific paper

10.1007/BF00761297

A functional integral representation is given for a large class of quantum mechanical models with a non--L2 ground state. As a prototype the particle in a periodic potential is discussed: a unique ground state is shown to exist as a state on the Weyl algebra, and a functional measure (spectral stochastic process) is constructed on trajectories taking values in the spectrum of the maximal abelian subalgebra of the Weyl algebra isomorphic to the algebra of almost periodic functions. The thermodynamical limit of the finite volume functional integrals for such models is discussed, and the superselection sectors associated to an observable subalgebra of the Weyl algebra are described in terms of boundary conditions and/or topological terms in the finite volume measures.

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