The fermion determinant in four-dimensional quantum electrodynamics in the
presence of O(2)XO(3) symmetric background gauge fields with a nonvanishing
global chiral anomaly is considered. It is shown that the leading mass
singularity of the determinant's nonperturbative part is fixed by the anomaly.
It is also shown that for a large class of such fields there is at least one
value of the fermion mass at which the determinant's nonperturbative part
reduces to its noninteracting value.Comment: This is an extended version of the author's paper in
Phys.Rev.D81(2010)10770