Lowest-order mass corrections for a (1+1)-dimensional Yukawa model in light-front perturbation theory

In this work we explicitly demonstrate the equivalence of covariant (Feynman) perturbation theory with noncovariant light-front perturbation theory (LEPT) for lowest-order self-energy corrections in the (1+1)-dimensional Yukawa model. We also perform calculations in oldfashioned perturbation theory in the infinite-momentum frame ($\mathrm{OFP}{\mathrm{T}}_{\infty }$) to elucidate the differences between LFPT and $\mathrm{OFP}{\mathrm{T}}_{\infty }$.