SU(2) Dirac-Yang-Mills quantum mechanics of spatially constant quark and gluon fields

TL;DR

This paper investigates the quantum mechanics of spatially constant SU(2) Yang-Mills-Dirac fields, deriving an unconstrained Hamiltonian, and calculates the low-energy spectrum, revealing a quark condensate and lower-energy states compared to pure gluons.

Contribution

It introduces a canonical transformation that Abelianises Gauss law constraints, simplifying the Hamiltonian for the coupled quark-gluon system in the strong coupling limit.

Findings

Lower energy ground state with quark condensate

Energy of sigma-antisigma excitation is about a fifth of the first glueball

Unconstrained Hamiltonian separates rotational and scalar degrees of freedom

Abstract

The quantum mechanics of spatially constant SU(2) Yang-Mills- and Dirac-fields minimally coupled to each other is investigated as the strong coupling limit of 2-color-QCD. Using a canonical transformation of the quark and gluon fields, which Abelianises the Gauss law constraints to be implemented, the corresponding unconstrained Hamiltonian and total angular momentum are derived. In the same way as this reduces the colored spin-1 gluons to unconstrained colorless spin-0 and spin-2 gluons, it reduces the colored spin-1/2 quarks to unconstrained colorless spin-0 and spin-1 quarks. These however continue to satisfy anti-commutation relations and hence the Pauli-exclusion principle. The obtained unconstrained Hamiltonian is then rewritten into a form, which separates the rotational from the scalar degrees of freedom. In this form the low-energy spectrum can be obtained with high accuracy. As an illustrative example, the spin-0 energy-spectrum of the quark-gluon system is calculated for massless quarks of one flavor. It is found, that only for the case of 4 reduced quarks (half-filling) satisfying the boundary condition of particle-antiparticle C-symmetry, states with energy lower than for the pure-gluon case are obtained. These are the groundstate, with an energy about 20% lower than for the pure-gluon case and the formation of a quark condensate, and the sigma-antisigma excitation with an energy about a fifth of that of the first glueball excitation.