open access

https://doi.org/10.14943/83653

https://hdl.handle.net/2115/69257

Instability in the spectral and the Fredholm properties of an infinite dimensional Dirac operator on the abstract Boson-Fermion Fock space

英語

strong coupling effect

2000-12-01

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

507

1-6

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.

紀要論文

Version of Record