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  • 1
    Electronic Resource
    Electronic Resource
    A Generalization of the Stone–Von Neumann Theorem to Nonregular Representations of the CCR-Algebra (1999)
    Springer
    Letters in mathematical physics 47 (1999), S. 307-320 
    Details
    ISSN: 1573-0530
    Keywords: Stone–von Neumann theorem ; Weyl algebra ; measurable representations.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give a classification, up to unitary equivalence, of the representations of the C*-algebra of the Canonical Commutation Relations which generalizes the classical Stone–von Neumann Theorem to the case of representations which are strongly measurable, but not necessarily strongly continuous. The classification includes all the (nonregular) representations which have been considered in physical models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007599222651
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Spectral stochastic processes arising in quantum mechanical models with a non-L 2 ground state (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 251-262 
    Details
    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
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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