QCD in terms of gauge-invariant dynamical variables

TL;DR

This paper reformulates low-energy QCD using gauge-invariant variables, enabling systematic strong-coupling expansions and accurate calculations of glueball masses, simplifying the complex non-Abelian gauge theory.

Contribution

It introduces a canonical transformation that Abelianizes Gauss-law constraints, leading to a gauge-invariant Hamiltonian expressed in terms of unconstrained, colorless glueball fields.

Findings

Leading-order approximation yields non-interacting hybrid-glueballs with calculable low-lying masses.

The reformulation simplifies the QCD Hamiltonian, separating rotational and scalar degrees of freedom.

Higher-order corrections systematically include interactions between glueballs.

Abstract

For a complete description of the physical properties of low-energy QCD, it might be advantageous to first reformulate QCD in terms of gauge-invariant dynamical variables, before applying any approximation schemes. Using a canonical transformation of the dynamical variables, which Abelianises the non-Abelian Gauss-law constraints to be implemented, such a reformulation can be achieved for QCD. The exact implementation of the Gauss laws reduces the colored spin-1 gluons and spin-1/2 quarks to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields and colorless Rarita-Schwinger fields respectively. The obtained physical Hamiltonian can then be rewritten into a form, which separates the rotational from the scalar degrees of freedom, and admits a systematic strong-coupling expansion in powers of lambda=g^{-2/3}, equivalent to an expansion in the number of spatial derivatives. The leading-order term in this expansion corresponds to non-interacting hybrid-glueballs, whose low-lying masses can be calculated with high accuracy by solving the Schr\"odinger-equation of the Dirac-Yang-Mills quantum mechanics of spatially constant physical fields (at the moment only for the 2-color case). Due to the presence of classical zero-energy valleys of the chromomagnetic potential for two arbitrarily large classical glueball fields (the unconstrained analogs of the well-known constant Abelian fields), practically all glueball excitation energy is expected to go into the increase of the strengths of these two fields. Higher-order terms in lambda lead to interactions between the hybrid-glueballs and can be taken into account systematically using perturbation theory in lambda.