Energy spectrum and the mass gap from nonperturbative quantization \`a la Heisenberg

TL;DR

This paper explores nonperturbative quantization of gauge fields with quarks, revealing solutions like spinballs and monopoles, and discusses their implications for the QCD vacuum, mass gaps, and deconfinement.

Contribution

It introduces approximate nonperturbative solutions involving gauge fields and quarks, connecting them to physical objects like glueballs and quantum fluctuations, with insights into the QCD vacuum structure.

Findings

Existence of regular solutions such as spinballs and monopoles.

Presence of mass gaps in the energy spectra of solutions.

Quantum QCD constant DQCD controls correlation length.

Abstract

Using approximate methods of nonperturbative quantization \`a la Heisenberg and taking into account the interaction of gauge fields with quarks, we find regular solutions describing the following configurations: (i) a spinball consisting of two virtual quarks with opposite spins; (ii) a quantum monopole; (iii) a spinball-plus-quantum-monopole system; and (iv) a spinball-plus-quantum-dyon system. A comparison with quasi-particles obtained by lattice and phenomenological analytical calculations is carried out. All these objects (except the spinball) are embedded in a bag created by the quantum coset condensate consisting of the SU(3)/(SU(2)~$\times$~U(1)) gauge fields. The existence of these objects is due to the Meissner effect, which implies that the SU(2)~$\times$~U(1) gauge fields are expelled from the condensate. The physical interpretation of these solutions is proposed in two different forms: (i) an approximate glueball model; and (ii) quantum fluctuations in the coset condensate of the nonperturbative vacuum or in a quark-gluon plasma. For the spinball and the spinball-plus-quantum-monopole configuration, we obtain energy spectra, in which mass gaps are present. The process of deconfinement is discussed qualitatively. It is shown that the quantum chromodynamics constant $\Lambda_{\text{QCD}}$ appears in the nonperturbative quantization \`a la Heisenberg as some constant controlling the correlation length of quantum fields in a spacelike direction.