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A few remarks on the zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges
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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.
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Cited by 3 Pith papers
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Birman-Schwinger Formulation of the Faddeev-Popov Zero-Mode Problem
The first Gribov horizon of a transverse gauge background equals the first appearance of −1 in the spectrum of a normalized Birman-Schwinger operator, via an inertia-preserving congruence rather than a similarity.
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Some Remarks on the Spectral Geometry of the Gribov Horizon
For the SU(2) hedgehog with h=9gr/(r^3+1)^2, the reduced Faddeev-Popov operator is positive exactly for -2<g<1, with normalizable threshold zero modes at both endpoints.
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On the consistency of Lorentz-Violating Yang-Mills theories: Gauge invariance and non-perturbative effects
A gauge-invariant massive extension of Lorentz-violating Yang-Mills theory is constructed, along with a BRST-invariant refined Gribov-Zwanziger action and its tree-level propagator.
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