Principles and Possibilities for Bound States in Gauge Theory
Abstract
Bound states differ from scattering yet are not covered in textbooks on Quantum Field Theory. I discuss a perturbative method for QED and QCD based on canonical quantization. Fully fixing temporal gauge A0(t,x)=0 imposes Gauss' law on physical states. As pointed out by Dirac, physical electrons have a longitudinal gauge field AL, whose energy is the instantaneous Coulomb potential. The situation is analogous for quarks and gluons in QCD. An instantaneous confining potential arises for color singlet q q states when a non-vanishing boundary condition on ALa(x∞) is specified in Gauss' constraint. As suggested by Gribov, αs(Q2) may freeze at a perturbative value when the confining potential dominates. Hadrons can then be calculated perturbatively. At vanishing quark mass there is a jPC=0++ state with zero energy which can mix with the perturbative vacuum, giving rise to a spontaneous breaking of chiral symmetry.
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