QCD in terms of gauge-invariant dynamical variables

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 λ = 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 Schrödinger-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 λ lead to interactions between the hybrid-glueballs and can be taken into account systematically using perturbation theory in λ . Xth Quark Confinement and the Hadron Spectrum

Unconstrained Hamiltonian formulation of low energy QCD

“…The corresponding unconstrained approach, a description in terms of gauge-invariant dynamical variables via an exact implementation of the Gaws laws, has been considered by many authors (o.a. [1], [4]- [11], and references therein) to obtain a non-perturbative description of QCD at low energy, as an alternative to lattice QCD. I shall first discuss in Sec.2 the unphysical, but technically much simpler case of 2-colors, and then show in Sec.3 and Sec.4 how the results can be generalised to SU(3).…”

“…such that the corresponding non-vanishing structure constants, [ τ a 2 , τ b 2 ] = ic abc τ c 2 , have at least one index ∈ {1, 2, 3}, the symmetric gauge of SU(2), Equ. (10), can be generalised to SU(3) [5,10,11],…”

“…2 , have at least one index ∈ {1, 2, 3}, the symmetric gauge of SU(2), Equ. (10), can be generalised to SU(3) [5,10,11],…”