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

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  • Asao Arai

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.

Suggested Citation

  • Asao Arai, 2014. "A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space," Journal of Mathematics, Hindawi, vol. 2014, pages 1-13, September.
    • Handle: RePEc:hin:jjmath:713690
    DOI: 10.1155/2014/713690
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