Quarks in a constant self-dual Euclidean background field: (II). Influence on the stability of the background field

Abstract

The fermionic determinant is expanded in powers of the oscillations around a semiclassical background gluon field. In the quadratic approximation, with a translation invariant (anti)self-dual background SU(2) gluon field, the changes of the zero eigenvalues are investigated in a perturbative approximation. Subtracting the field-idependent contributions, the eigenvalue of the “color-longitudinal” zero mode is unchanged while those of the “color-transverse” zero modes get positive shifts, suggesting a further stabilization of the gluonic oscillations.