ISSN:
1573-0530
Keywords:
81S40
;
60G20
;
46J10
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
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 (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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00761297
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