The non-perturbative BRST quartets generated by transverse gluons or quarks in Landau gauge

TL;DR

This paper reviews the non-perturbative BRST quartet mechanism in Landau gauge, focusing on the role of transverse gluons and quarks, and derives Bethe-Salpeter equations to explore bound states within these quartets.

Contribution

It introduces the field contents of non-perturbative BRST quartets generated by gluons and quarks, and derives Bethe-Salpeter equations to investigate their bound state nature.

Findings

Bethe-Salpeter equations suggest bound states as daughter states in non-perturbative BRST quartets.

Infrared divergence of the quark-gluon vertex supports the existence of these bound states.

The scaling solution ensures infrared consistency of the Bethe-Salpeter equations.

Abstract

The BRST quartet mechanism is briefly reviewed. A special emphasis is given to the distinction of perturbative versus non-perturbative quartets. The field contents of the non-perturbative BRST quartets generated by transverse gluons or quarks in Landau gauge are presented. Corresponding truncated Bethe-Salpeter equations for the respective first daughter and second parent states are derived. It is discussed in which sense these equations provide evidence for the existence of bound states as daughter states in non-perturbative BRST quartets. It is noted that within the scaling solution of functional approaches the infrared divergence of the quark-gluon vertex is exactly the right one tomake the respective Bethe-Salpeter equation infrared consistent.