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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/713690 |
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| author | Asao Arai |
| author_facet | Asao Arai |
| author_sort | Asao Arai |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7963e6b581834fc68808ca4e9472dcc4 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-7963e6b581834fc68808ca4e9472dcc42025-02-03T01:00:03ZengWileyJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/713690713690A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock SpaceAsao Arai0Department of Mathematics, Hokkaido University, Sapporo 060-0810, JapanSpectral 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.http://dx.doi.org/10.1155/2014/713690 |
| spellingShingle | Asao Arai A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space Journal of Mathematics |
| title | A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space |
| title_full | A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space |
| title_fullStr | A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space |
| title_full_unstemmed | A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space |
| title_short | A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space |
| title_sort | special class of infinite dimensional dirac operators on the abstract boson fermion fock space |
| url | http://dx.doi.org/10.1155/2014/713690 |
| work_keys_str_mv | AT asaoarai aspecialclassofinfinitedimensionaldiracoperatorsontheabstractbosonfermionfockspace AT asaoarai specialclassofinfinitedimensionaldiracoperatorsontheabstractbosonfermionfockspace |