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

الملخص EN

Spectral properties of a special class of infinite dimensional Dirac operators Q(α) on the abstract boson-fermion Fock space ℱ(ℋ,?) associated with the pair (ℋ,?) 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,?) is discussed.