- 96-489 Schmitt T.
- The Cauchy Problem for Abstract Evolution Equations
with Ghost and Fermion Degrees of Freedom
(105K, LateX2E + AMSLaTeX)
Oct 14, 96
(auto. generated ps),
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Abstract. We consider a class of abstract nonlinear evolution equations in
supermanifolds (smf's) modelled over Z_2-graded locally convex
spaces. We show uniqueness, local existence, smoothness, and an
abstract version of causal propagation of the solutions. If an a-priori
estimate prevents the solutions from blowing-up then an
infinite-dimensional smf of "all" solutions can be constructed.
We apply our results to a class of systems of nonlinear field
equations with anticommuting fields which 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.