  For nonlinear sigma-models in the unitary symmetry class, the non-linear
target space can be parameterized with cubic polynomials. This choice of
coordinates has been known previously as the Dyson-Maleev parameterization for
spin systems, and we show that it can be applied to a wide range of
sigma-models. The practical use of this parameterization includes
simplification of diagrammatic calculations (in perturbative methods) and of
algebraic manipulations (in non-perturbative approaches). We illustrate the use
and specific issues of the Dyson-Maleev parameterization with three examples:
the Keldysh sigma-model for time-dependent random Hamiltonians, the
supersymmetric sigma-model for random matrices, and the supersymmetric
transfer-matrix technique for quasi-one-dimensional disordered wires. We
demonstrate that nonlinear sigma-models of unitary-like symmetry classes C and
B/D also admit the Dyson-Maleev parameterization.
