Boundary Surface Term In QCD Is At Finite Distance Due To Confinement of Quarks and Gluons Inside Finite Size Hadron

TL;DR

This paper demonstrates that the boundary surface term in QCD is finite and non-zero due to quark and gluon confinement within hadrons, affecting the cluster decomposition property.

Contribution

It establishes that the boundary surface term in QCD is at finite distance and non-zero, providing insight into confinement effects and the failure of cluster decomposition.

Findings

Boundary surface term in QCD is at finite distance.

Boundary surface term remains non-zero regardless of field dependence.

Confinement causes the failure of cluster decomposition in QCD.

Abstract

In this paper we show that since we have not observed quarks and gluons outside the hadron due to the confinement of quarks and gluons inside the hadron, the boundary surface term in QCD is at the finite distance which is at the surface of the finite size hadron. Since the boundary surface is at the finite distance we find that the boundary surface term in QCD is non-zero irrespective of the form of the $r$ dependence of the gluon field ${\hat A}_\mu^a(t,r)$ and the $r$ dependence of the quark field ${\hat \psi}_i(t,r)$ where $a=1,...,8$ and $i=1,2,3$ are the color indices. We show that this is consistent with the fact that the cluster decomposition property fails in QCD due to confinement.