Two-fermion bound-state equation using light-front Tamm-Dancoff field theory in 3+1 dimensions

Attention has recently been paid to light-front Tamm-Dancoff field theory in 1+1 dimensions, including the proposition of a sector-dependent renormalization procedure. We extend this formalism to 3+1 dimensions, and examine a two-fermion system using light-front field theory in the lowest nontrivial Tamm-Dancoff approximation. It is found that the extension to 3+1 dimensions results in an integral equation with a kernel which does not decrease rapidly enough to admit solutions for $L_3=0\mathrm{}$ states.