Schmitt T.
The Cauchy Problem for Classical Field Equations
with Ghost and Fermion Fields
(141K, LateX2E + AMSLaTeX)

ABSTRACT.  Using a supergeometric interpretation of field functionals
developed in previous papers,
we show that for quite a large class of systems of nonlinear
field equations with anticommuting fields, infinite-dimensional 
supermanifolds (smf) of classical solutions can be constructed. 
Such systems arise in classical field models used for realistic 
quantum field theoretic models.
In particular, we show that under suitable conditions,
the smf of smooth Cauchy data with compact support
is isomorphic with an smf of corresponding classical solutions 
of the model.