Chiral symmetry breaking and quark confinement in the nilpotency expansion of QCD

TL;DR

This paper introduces a bosonization approach in lattice QCD using the nilpotency expansion, revealing insights into chiral symmetry breaking and quark confinement through a saddle point analysis.

Contribution

It develops a novel nilpotency expansion method in lattice QCD that connects bosonization with confinement and chiral symmetry breaking phenomena.

Findings

Fermionic quasiparticles are confined as color singlets.

Conditions for chiral symmetry breaking are identified.

A framework for deriving meson-nucleon interactions is outlined.

Abstract

We apply to lattice QCD a bosonization method previously developed in which dynamical bosons are generated by time-dependent Bogoliubov transformations. The transformed action can be studied by an expansion in the inverse of the nilpotency index, which is the number of fermionic states in the structure function of composite bosons. When this number diverges the model is solved by the saddle point method which has a variational interpretation. We give a stationary covariant solution for a background matter field whose fluctuations describe mesons. In the saddle point approximations live fermionic quasiparticles with quark quantum numbers which are confined, in the sense that they propagate only in pointlike color singlets. Conditions for chiral symmetry breaking are determined, to be studied numerically, and a derivation of mesons-nucleons action is outlined.