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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

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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
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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