On the zero modes of the Faddev-Popov operator in the Landau gauge

Abstract

Following Henyey procedure, we construct examples of zero modes of the Faddev-Popov operator in the Landau gauge in Euclidean space in D dimensions, for both SU(2) and SU(3 groups. We consider gauge field configurations $A_{\mu }^a$ which give rise to a field strength, $F_{\mu \nu }^a={\partial }_{\mu }{A}_{\nu }^a-{\partial }_{\nu }{A}_{\mu }^a+f^{abc}{A}_{\mu }^b{A}_{\nu }^c$, whose nonlinear term, $f^{abc}{A}_{\mu }^b{A}_{\nu }^c$, turns out to be nonvanishing. To our knowledge, this is the first time where such a non-abelian configuration is explicitly obtained in the case of SU(3) in 4D.

14 page,no figures

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