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Instability in the spectral and the Fredholm properties of an infinite dimensional Dirac operator on the abstract Boson-Fermion Fock space
| Title: | Instability in the spectral and the Fredholm properties of an infinite dimensional Dirac operator on the abstract Boson-Fermion Fock space |
| Authors: | Arai, A. Browse this author |
| Keywords: | Boson-Fermion Fock space | | supersymmetric quantum field | | infinite dimensional Dirac operator | | non-regular perturbation | | kernel | | spectrum | | Fredholm property | | strong coupling effect |
| Issue Date: | 1-Dec-2000 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 507 |
| Start Page: | 1 |
| End Page: | 6 |
| Abstract: | A perturbed Dirac operator Q(a) on the abstract Boson-Fermion Fock space is considered, where a E C is a perturbation ( coupling) parameter and the unperturbed operator Q(0) is taken to be a free infinite dimensional Dirac operator introduced by the author ( A. Arai, J. Funct. Anal. 105(1992), 342-408). The following results are reported: (i) Under some conditions, the kernel of Q(a) is one dimensional for all a f:. ao with some ao f:. 0 and degenerate at a = a0, while, under another condition, the kernel of Q(a) is one dimensional for all a E C. (ii) There are cases where, for all sufficiently large la I with a < 0, Q( a) has infinitely many non-zero eigenvalues even if Q(0) has no non-zero eigenvalues. This is a strong coupling effect. (iii) Fredholm property of Q (a) also depends on the coupling parameter a. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69257 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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