Study of the zero modes of the Faddeev-Popov operator in the maximal Abelian gauge

D. G. Tedesco; M. A. L. Capri; M. S. Guimaraes; S. P. Sorella; V. E. R. Lemes

Study of the zero modes of the Faddeev-Popov operator in the maximal Abelian gauge

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arxiv 1309.4043 v1 pith:KC4RCHKA submitted 2013-09-16 hep-th

Study of the zero modes of the Faddeev-Popov operator in the maximal Abelian gauge

M. A. L. Capri , M. S. Guimaraes , V. E. R. Lemes , S. P. Sorella , D. G. Tedesco This is my paper

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keywords gaugemodeszeroabelianeuclideanfaddeev-popovfinitemaximal

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A study of the zero modes of the Faddeev-Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2) and for different Euclidean space-time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: i) the finite Euclidean Yang-Mills action, ii) the finite Hilbert norm.

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Some Remarks on the Spectral Geometry of the Gribov Horizon
hep-th 2026-07 accept novelty 6.0

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.