Renormalization of Tamm-Dancoff Integral Equations

Details Renormalization of Tamm-Dancoff Integral Equations Renormalization of Tamm-Dancoff Integral Equations

1992-10-28

arxiv.org/abs/hep-th/9210147v1

Phys.Rev. D46 (1992) 5479-5486

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, OHSTPY-HEP-T-92-014

Scientific paper

10.1103/PhysRevD.46.5479

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, non-perturbative 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 generates 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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