1996/10/14 by Thomas Schmitt, Thomas P. Schmitt, Schmitt, Thomas · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows #dg-ga #hep-th #math.DG
paper · pdf · doi:10.48550/arxiv.hep-th/9610096
28 pages, LateX2E+AMSLaTeX
arxiv created 1996/10/14 · arxiv updated 2009/11/30
We consider a class of abstract nonlinear evolution equations in supermanifolds (smf's) modelled over Z2-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.