Disentangling intertwined embedded states and spin effects in light-front quantization

The common belief of equivalence between the manifestly covariant calculation and the LF (light-front) calculation linked by the LF energy integration of the Feynman amplitude is not always realized. Our example of a light-front calculation with a fermion loop explicitly shows that the persistent end-point singularity in the nonvalence contribution to the bad component of the current ${J}^{\ensuremath{-}}$ leads to an infinitely different result from that obtained by the covariant Feynman calculation unless the divergence is properly subtracted. Ensuring the equivalence to the Feynman amplitude, we have identified the divergent term that needs to be removed from ${J}^{\ensuremath{-}}.$ Only after this term is subtracted is the result covariant and then it satisfies current conservation. The same calculation with the boson loop, however, does not exhibit such a singular behavior and without any adjustment yields a result identical to the Feynman amplitude. Numerical estimates of the nonvalence contributions are presented for the cases of both fermion and boson constituents.