Birman-Schwinger Formulation of the Faddeev-Popov Zero-Mode Problem

Daniel G. Tedesco

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arXiv · 2607.14425

Birman-Schwinger Formulation of the Faddeev-Popov Zero-Mode Problem

Daniel G. Tedesco

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Abstract

After removing the constant adjoint modes associated with global gauge rotations, we recast the Landau-gauge Faddeev-Popov zero-mode problem in Birman-Schwinger form on a periodic domain. The construction yields a self-adjoint Faddeev-Popov realization under the stated regularity assumptions and a normalized operator with a fixed spectral criterion for the first Gribov horizon. The same formulation relates the horizon condition to the ghost resolvent at fixed gauge background while distinguishing fixed-background spectral information from ensemble-averaged propagators. For a periodic transverse background in SU(2) Yang-Mills theory, the zero-mode equation reduces to a Mathieu problem, allowing the horizon threshold to be determined independently through spectral and finite-channel methods. The construction also yields explicit volume dependence for the critical background and its classical action.

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Daniel G. Tedesco. 2026-07-15. Birman-Schwinger Formulation of the Faddeev-Popov Zero-Mode Problem. https://arxiv.org/abs/2607.14425

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