Abstract
A program to utilize the Tamm-Dancoff approximation, on the light front, to solve relativistic quantum field theories, is presented. We present a well-defined renormalization program for the Tamm-Dancoff approximation. This renormalization program utilizes a Minkowski space version of Wilson's renormalization group. We study light-front ${\mathrm{\ensuremath{\varphi}}}^{4}$ field theory in (3+1) dimensions, within a two-particle truncation of Fock space. We further simplify our calculations by considering only one marginal operator and one irrelevant operator. The renormalization procedure requires no more marginal or relevant operators. We derive an effective, renormalized, Hamiltonian. These techniques may be germane to the effort to find an effective, low-energy, light-front Hamiltonian for quantum chromodynamics.
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