Possible Consequences of Conjectural Periodicity of Spectrum of Lattice Dirac Operator

Physics – High Energy Physics – High Energy Physics - Lattice

Scientific paper

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17 pages, Latex2e

Scientific paper

Some consequences which follow from the periodicity assumption for spectral density of Wilson--Dirac operator are studied. Such an assumption allows to obtain simple representations for quark propagator, which reveals an important role of $m\leftrightarrow -m$ symmetry. It is argued that this symmetry is restored when the mirror fermion mass $m_r$ tended to infinity. The constrains on zero modes of Wilson--Dirac operator in a toy model approximation are also discussed.

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