A Perturbative Gluon Condensate?

Abstract

I propose that the properties of QCD perturbation theory should be investigated when the boundary state (`perturbative vacuum') at $t= \pm\infty$ includes gluons. Any boundary state that has an overlap with the true QCD ground state generates a perturbative series that (when summed to all orders) is formally exact. Through an analogy with the boundary condition corresponding to a fermion condensate, I propose an explicit form for a `perturbative gluon condensate' that suppresses low momentum gluon production, thus generating an effective mass gap. Standard perturbative calculations are modified only through a change in the $i\epsilon$ prescription of low momentum $(|\pv| \lsim \Lambda_{QCD})$ gluon propagators. Gauge invariance is expected to be preserved since this modification is equivalent to adding on-shell external particles. Renormalizability is unaffected since only low-momentum propagators are modified. Due to the asymptotic low momentum gluons boost invariance is not explicit. Lorentz invariance should be restored in the sum to all orders in analogy to standard bound state calculations.