A few remarks on the zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges

摘要

The construction outlined by Henyey [Phys. Rev. D 20, 1460 (1979)] is employed to provide examples of normalizable zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges in SU(2) Euclidean Yang-Mills theories in d = 3 dimensions. The corresponding gauge configurations have all finite norm ||A||~2 < ∞. In particular, in the case of the Landau gauge, the explicit construction of an infinite class of normalizable zero modes with finite norm ||A||~2 is provided.