Renormalization of Tamm-Dancoff integral equations

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Abstract
During the last few years, interest has arisen in using light-front Tamm-Dancoff field theory to describe relativistic bound states for theories such as QCD. Unfortunately, difficult renormalization problems stand in the way. We introduce a general, nonperturbative approach to renormalization that is well suited for the ultraviolet and, presumably, the infrared divergences found in these systems. We reexpress the renormalization problem in terms of a set of coupled inhomogeneous integral equations, the "counterterm equation." The solution of this equation provides a kernel for the Tamm-Dancoff integral equations which generate states that are independent of any cutoffs. We also introduce a Rayleigh-Ritz approach to numerical solution of the counterterm equation. Using our approach to renormalization, we examine several ultraviolet-divergent models. Finally, we use the Rayleigh-Ritz approach to find the counterterms in terms of allowed operators of a theory.
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