Ghosts Hunting in the Yang-Mills Vacuum

Seth Grable

Ghosts Hunting in the Yang-Mills Vacuum

High Energy Physics - Theory 2026-07-08 v1 Mathematical Physics Nuclear Theory

Authors: Seth Grable

Abstract

In this work I analyze the zero-modes of a one-loop semi-classical Yang-Mills theory in $3+1d$ . I find the zero-modes are generated by gauge redundancy of the background field. With proper gauge fixing, via the introduction of a bosonic ghost term, and the use of zeta-function regularization, a finite one-loop effective theory is calculated in closed form, reproducing the well known one-loop Yang-Mills beta-function.

Keywords

yang-mills vacuum zero-modes ghost field zeta-function regularization one-loop effective theory beta-function

Cite

@article{arxiv.2607.07954,
  title  = {Ghosts Hunting in the Yang-Mills Vacuum},
  author = {Seth Grable},
  journal= {arXiv preprint arXiv:2607.07954},
  year   = {2026}
}