Fixed sources in light-front dynamics and Wilson's model of coupling-constant renormalization

Abstract

We construct a fixed source model of nonperturbative coupling-constant renormalization in light-front dynamics as a limit of a theory of heavy fermionic sources when the fermion mass becomes very large. We begin with the canonical light-front Hamiltonian for Yukawa quantum field theory. We introduce cutoffs and consider the limit when the fermion mass is much larger than the momentum cutoffs. We then derive an effective Hamiltonian in the Fock space spanned by sectors with only one fermion and arbitrarily many bosons. The total momentum of the dressed fermionic source is separated from the internal dynamics of the system. The effective Hamiltonian for the internal dynamics is shown to be equivalent to the original fixed source model Hamiltonian considered by Wilson. Wilson's nonperturbative renormalization-group analysis applies to the light-front version of the model. The new feature of the light-front model is the appearance of manifest boost invariance, which allows one to study a heavy fermion source with arbitrary momentum. We discuss the generalization of the renormalization-group analysis to the case where the fermion mass is comparable to the boson mass.