On the spectral flow of the hermitian Dirac–Wilson operator
نویسنده
چکیده
The spectral flow of the hermitian Dirac–Wilson operator H(m) has been used to construct a lattice version of the index of the Dirac operator. We clarify some aspects of this construction by showing the following (in 4D): When the curvature of the lattice gauge field satisfies an approximate smoothness condition, crossings of the origin by eigenvalues of H(m) can only happen when m is close to 0,2,4,6 or 8. The relevant spectral flow comes from the crossings with m close to 0; the other crossings are due to “approximate doubler” fields.
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Spectrum of the Hermitian Wilson Dirac operator
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