Origin of Confining Force
Abstract
In this article we present exact calculations that substantiate a clear picture relating the confining force of QCD to the zeromodes of the FaddeevPopov (FP) operator $\mathcal{M}(A) =  \partial \cdot D(A)$. This is done in two steps. First we calculate the spectral decomposition of the FP operator and show that the ghost propagator $\mathcal{G}(k; A) = \langle \vec{k} \mathcal{M}^{1}(A)  \vec{k} \rangle$ in an external gauge potential $A$ is enhanced at low $k$ in Fourier space for configurations $A$ on the Gribov horizon. This results from the new formula in the low$k$ regime $\mathcal{G}^{ab}(k,A) = \delta^{ab} \lambda_{\vec{k}}^{1}(gA)$, where $\lambda_{\vec{k}}(gA)$ is the eigenvalue of the FP operator that emerges from $\lambda_{\vec{k}}(0) = \vec{k}^2$ at $A$ = 0. Next we derive a strict inequality signaling the divergence of the colorCoulomb potential at low momentum $k$ namely, $\widetilde{\mathcal{V}}(k) \geq k^2 G^2(k)$ for $k \to 0$, where $\widetilde{\mathcal{V}}(k)$ is the Fourier transform of the colorCoulomb potential $\mathcal{V}(r)$ and $G(k)$ is the ghost propagator in momentum space. The first result holds in the Landau and Coulomb gauges, whereas the second holds in the Coulomb gauge only. We propose a new numerical lattice gauge fixing that should be closer to the present analytic approach than other numerical gauges.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 DOI:
 10.48550/arXiv.1512.05725
 arXiv:
 arXiv:1512.05725
 Bibcode:
 2015arXiv151205725C
 Keywords:

 High Energy Physics  Theory
 EPrint:
 Phys. Rev. D 93, 105024 (2016)