arXiv subjects

Daniel G. Tedesco

Publications and source records attributed to Daniel G. Tedesco.

3 recordsLinked to original sources

arXiv2026

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

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.

hep-th↗

arXiv2026

Blind Spots of the Zwanziger Horizon Function

We examine the configurationwise relation between the first Gribov horizon, defined by loss of positivity of the Faddeev-Popov operator, and Zwanziger's horizon function, which probes the inverse operator through background-dependent sources. The analysis focuses on whether the spectral directions associated with the onset of the Gribov horizon are necessarily accessible to the sources entering the horizon function, including situations in which the critical subspace is degenerate. This question is studied for radial SU(2) hedgehog backgrounds in three and four Euclidean dimensions, where angular symmetry constrains the source sector while the radial profile controls the ordering of Faddeev-Popov thresholds. Variational estimates and finite-volume calculations are used to characterize the threshold structure for smooth radial profiles. The regular-gauge BPST background is treated separately because of domain issues associated with zero-energy behavior and the horizon source in the full-space setting. The discussion is restricted to configurationwise spectral properties and does not address the statistical weighting of these backgrounds in the Yang-Mills functional integral.

hep-lat↗

arXiv2026

Some Remarks on the Spectral Geometry of the Gribov Horizon

We develop a local spectral framework for the Landau-gauge Gribov horizon that distinguishes gauge-orbit projection from degeneracy of the gauge-fixing Hessian. On a flat torus, spatially constant ghosts form a residual global-color kernel; after removal of this kernel, the reduced Faddeev-Popov operator is the normal Morse-Bott Hessian of the orbit-norm functional, whereas the covariant Laplacian defines the orthogonal connection. For the associated affine focal pencil, we prove a quadratic-form index theorem with a Morse-Bott endpoint. At a regular isolated crossing, the critical projector $P$ and invertible compressed derivative $Γ=P\dot{\mathcal{M}}P$ determine the spectral-flow jump and leading Laurent coefficient of the sourced ghost resolvent; for a simple zero, they also give the wall conormal. Crossings reached along affine rays from the positive region have negative-definite $Γ$, including symmetry-protected multiplets, while a second Schur reduction determines pole orders along tangential paths. A projected single-harmonic model checks the projected Feynman-Hellmann relation. For an $SU(2)$ hedgehog on $\mathbb R^3$, we construct a normalizable threshold state in every coupled spin-orbit channel and minimize over the full tower to obtain the exact stability interval $-2<g<1$. Dirichlet-box spectra approach these thresholds and serve as finite-volume comparisons; no numerical fit enters the continuum result.

hep-th↗