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

Asao Arai

Journal of Mathematics, 2014, vol. 2014, 1-13

Abstract:

Spectral properties of a special class of infinite dimensional Dirac operators on the abstract boson-fermion Fock space associated with the pair of complex Hilbert spaces are investigated, where is a perturbation parameter (a coupling constant in the context of physics) and the unperturbed operator is taken to be a free infinite dimensional Dirac operator. A variety of the kernel of is shown. It is proved that there are cases where, for all sufficiently large with , has infinitely many nonzero eigenvalues even if has no nonzero eigenvalues. Also Fredholm property of restricted to a subspace of is discussed.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:713690

DOI: 10.1155/2014/713690

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