MHV Lagrangian for N=4 Super Yang-Mills

Here we formulate two field redefinitions for N=4 Super Yang-Mills in light cone superspace that generates only MHV vertices in the new Lagrangian. After careful consideration of the S-matrix equivalence theorem, we see that only the canonical transformation gives the MHV Lagrangian that would correspond to the CSW expansion. Being in superspace, it is easier to analyse the equivalence theorem at loop level. We calculate the on shell amplitude for 4pt $(\bar{\Lambda}\bar{{\rm A}}\Lambda {\rm A})$ MHV in the new lagrangian and show that it reproduces the previously known form. We also briefly discuss the relationship with the off-shell continuation prescription of CSW.