 95121 J.Loeffelholz, G.Morchio, F.Strocchi
 Spectral stochastic processes arising in quantum mechanical models
with a nonL^2 ground state
(41K, tex)
Feb 24, 95

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Abstract. A functional integral representation is given for a
large class of quantum mechanical models with a non$L^2$ 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 ({\it 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 \lq\lq observable\rq\rq\ 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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