Renormalized nonperturbative fermion model in covariant light-front dynamics

Abstract

Within the framework of the covariant formulation of light-front dynamics, we develop a nonperturbative renormalization scheme in the fermion model supposing that the composite fermion is a superposition of the ``bare'' fermion and a fermion+boson state. We first assume the constituent boson to be spinless. Then we address the case of gauge bosons in the Feynman and in the light-cone gauges. For all these cases the fermion state vector and the necessary renormalization counterterms are calculated analytically. It turns out that, in light-front dynamics, to restore the rotational invariance, an extra counterterm is needed, having no analogue in the Feynman approach. For gauge bosons the results obtained in the two gauges are compared with each other. In general, the number of spin components of the two-body $(\mathrm{fermion}+\mathrm{boson})$ wave function depends on the gauge. But due to the two-body Fock space truncation, only one nonzero component survives for each gauge. And moreover, the whole solutions for the state vector, found for the Feynman and light-cone gauges, are the same (except for the normalization factor). The counterterms are, however, different.