Supermanifolds of classical solutions for Lagrangian field models with ghost and fermion fields

Using a supergeometric interpretation of field functionals, we show that for a class of classical field models used for realistic quantum field theoretic models, an infinite-dimensional supermanifold (smf) of classical solutions in Minkowski space can be constructed. That is, we show that the smf of smooth Cauchy data with compact support is isomorphic with an smf of corresponding classical solutions of the model.