Birman-Schwinger Formulation of the Faddeev-Popov Zero-Mode Problem
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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BibTeX
@misc{tedesco2026birmanschwinger,
title = {{Birman-Schwinger Formulation of the Faddeev-Popov Zero-Mode Problem}},
author = {Daniel G. Tedesco},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.14425},
eprint = {2607.14425},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.14425},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Birman-Schwinger Formulation of the Faddeev-Popov Zero-Mode Problem
AU - Daniel G. Tedesco
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2607.14425
UR - https://arxiv.org/abs/2607.14425
AB - 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.
ER -