  Supersymmetric gauge theories are characterized by the existence of a
transformation of the bosonic fields (Nicolai map) such that the Jacobi
determinant of the transformation equals the product of the
Matthews-Salam-Seiler and Faddeev-Popov determinants. This transformation had
been worked out to second order in the coupling constant. In this paper, we
extend this result (and the framework itself) to third order in the coupling
constant. A diagrammatic approach in terms of tree diagrams, aiming to extend
this map to arbitrary orders, is outlined. This formalism bypasses entirely the
use of anti-commuting variables, as well as issues concerning the
(non-)existence of off-shell formulations for these theories. It thus offers a
fresh perspective on supersymmetric gauge theories and, in particular, the
ubiquitous $\mathcal N{=}\,4$ theory.
