A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space
A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space
Spectral properties of a special class of infinite dimensional Dirac operators<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>Q</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>α</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>on the abstract boson-fermion Fock space<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>ℱ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ℋ</mml:mi><mml:mo>,</mml:mo><mml:mi>𝒦</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>associated with the pair<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mo stretchy="false">(</mml:mo><mml:mi>ℋ</mml:mi><mml:mo>,</mml:mo><mml:mi>𝒦</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>of complex Hilbert spaces are investigated, where<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mi>α</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant="double-struck">C</mml:mi></mml:math>is a perturbation parameter (a coupling constant in the context of …