  Quantum correlators of pure supersymmetric Yang-Mills theories in D=3,4,6 and
10 dimensions can be reformulated via the non-linear and non-local
transformation (`Nicolai map') that maps the full functional measure of the
interacting theory to that of a free bosonic theory. As a special application
we show that for the maximally extended N=4 theory in four dimensions, and up
to order O(g^2), all known results for scalar correlators can be recovered in
this way without any use of anti-commuting variables, in terms of a purely
bosonic and ghost free functional measure for the gauge fields. This includes
in particular the dilatation operator yielding the anomalous dimensions of
composite operators. The formalism is thus competitive with more standard
perturbative techniques.
