A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space

Spectral properties of a special class of infinite dimensional Dirac operators Q(α) on the abstract boson-fermion Fock space ℱ(ℋ,𝒦) associated with the pair (ℋ,𝒦) of complex Hilbert spaces are investigated, where α∈C is a perturbation parameter (a coupling constant in the context of physics) and the...

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Bibliographic Details
Main Author: Asao Arai
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2014/713690
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Summary:Spectral properties of a special class of infinite dimensional Dirac operators Q(α) on the abstract boson-fermion Fock space ℱ(ℋ,𝒦) associated with the pair (ℋ,𝒦) of complex Hilbert spaces are investigated, where α∈C is a perturbation parameter (a coupling constant in the context of physics) and the unperturbed operator Q(0) is taken to be a free infinite dimensional Dirac operator. A variety of the kernel of Q(α) is shown. It is proved that there are cases where, for all sufficiently large |α| with α<0, Q(α) has infinitely many nonzero eigenvalues even if Q(0) has no nonzero eigenvalues. Also Fredholm property of Q(α) restricted to a subspace of ℱ(ℋ,𝒦) is discussed.
ISSN:2314-4629
2314-4785