Abstract
Hamiltonian theories with fermions are proved to be equivalent to hierarchies of ordinary Hamiltonian theories. The corresponding Poisson brackets are defined in terms of the original super-Poisson structure, while Hamiltonian functions are simply the coefficients in the expansion of the super-Hamiltonian function as a formal power series in Grassman generators. Fermion extensions of the KdV equation are considered to illustrate the general result; its space-supersymmetric extensions are used to show in particular how supersymmetry transformations can be recast as ordinary Hamiltonian symmetries.
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