Ghosts that Connect
摘要
The Faddeev-Popov procedure poses two conceptual puzzles. Puzzle (1): if gauge-equivalent configurations represent the same physics, the quotient F/G should suffice to compute physical amplitudes --- yet the procedure requires anti-commuting auxiliary fields, the ghosts, with no analogue on the quotient. What structure of F do they encode? Puzzle (2): gauge-fixing was supposed to eliminate local gauge symmetry, yet the gauge-fixed theory retains BRST --- a residual symmetry that acts on the gauge potential as an infinitesimal gauge transformation. Why does it survive? Both puzzles dissolve together. Following Dougherty2021 and DoughertyRead2026, I take ghosts to encode classical content of F → F/G, but identify a different structure: a principal connection π on this bundle. The ghost is π; the BRST operator is the vertical exterior derivative on field space; the Maurer-Cartan equation is its vertical Cartan structure equation. The Faddeev-Popov calculus draws only on π's vertical content, which the algebraic reading also captures; π's horizontal content, on which the Vilkovisky-DeWitt programme rests, supplies the cross-orbit pairing that gauge-fixing, dressing-based quantisation, and counterfactual comparison require and the quotient discards. BRST is the rigid, vertical symmetry that preserves this pairing; this is why it survives gauge-fixing.
引用
@article{arxiv.2607.27297,
title = {Ghosts that Connect},
author = {Henrique Gomes},
journal= {arXiv preprint arXiv:2607.27297},
year = {2026}
}