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

Abstract

The construction outlined by Henyey 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 < \infty. 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.

Comments: 9 pages. Extended discussion in the conclusions. Version accepted for publication in the J. Math. Phys