QCD at large and short distances

TL;DR

This paper presents a divergence-free formulation of QCD that encompasses both perturbative and non-perturbative phenomena, analyzing its implications for asymptotic freedom, chiral symmetry breaking, and related problems.

Contribution

It introduces a divergence-free formulation of QCD that includes both perturbative and non-perturbative effects, offering new insights into its foundational structure.

Findings

QCD can be formulated without divergences or renormalization

The theory's non-uniqueness due to asymptotic freedom is demonstrated

Chiral symmetry breaking and the U(1) problem are analyzed within this framework

Abstract

The formulation of QCD which contains no divergences and no renormalization procedure is presented. It contains both perturbative and non-perturbative phenomena. It is shown that, due to its asymptotically free nature, the theory is not defined uniquely. The chiral symmetry breaking and the nature of the octet of pseudo-scalar particles as quasi-Goldstone states are analysed in the theory with massless and massive quarks. The U(1) problem is discussed.