The Mass Gap Approach to QCD.I. The true gauge and dynamical structures of its ground state

TL;DR

This paper proves that a non-trivial quantum Yang-Mills theory, such as QCD, must have a positive mass gap, by deriving a novel constraint on solutions using Slavnov-Taylor identities and analyzing the gluon propagator.

Contribution

It introduces a new constraint on QCD solutions, demonstrating the necessity of a mass gap and clarifying the role of the tadpole term in the gluon self-energy.

Findings

Proves the existence of a positive mass gap in QCD.

Derives a unique constraint on solutions using Slavnov-Taylor identities.

Shows the mass gap cannot be ignored in the ground state of QCD.

Abstract

Assuming that a non-trivial quantum Yang-Mills theory exists, we have proved that it should have a mass gap $\Delta^2 > 0$, indeed. The proof is based on the derivation of the novel constraint on any solution to QCD. It has been exactly and uniquely derived in the framework of the Slavnov-Taylor identities for the gauge particles Green's functions (propagators), involving the equation of motion for the full gluon propagator as well. The novel constraint has the two different solutions, coinciding only at high energies. The dynamical source of this difference has to be identified with the constant tadpole term, contributing to the full gluon self-energy. Just its renormalized version is conventionally called a mass gap. We prove that it cannot be disregarded from the theory and its ground state by any means. The perturbative renormalizability of QCD will not be affected by a new solution for the gluon equation of motion. We also provide the formulation of the self-consistency condition for the gauge choice in QCD. Finally, we discuss the interrelation of our advance results with the Jaffe-Witten's theorem.