Hamiltonian Light-Front Field Theory and Quantum Chromodynamics

Abstract

Light-front coordinates offer a scenario in which a constituent picture of hadron structure can emerge from QCD, after several difficulties are addressed. Field theoretic difficulties force us to introduce cutoffs that violate Lorentz covariance and gauge invariance, and a new renormalization group formalism based on a similarity transformation is used with coupling coherence to fix cuonterterms that restore these symmetries. The counterterms contain functions of longitudinal momentum fractions that severely complicate renormalization, but they also offer possible resolutions of apparent contradictions between the constituent picture and QCD. The similarity transformation and coupling coherence are applied to QED; and it is shown that the resultant Hamiltonian leads to standard lowest order bound state results, with the Coulomb interaction emerging naturally. The same techniques are applied to QCD and with physically motivated assumptions it is shown that a simple confinement mechanism appears.