The Cauchy Problem for Classical Field Equations with Ghost and Fermion Fields

1996/07/16 by Thomas Schmitt, Thomas P. Schmitt, Schmitt, Thomas
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #dg-ga #hep-th #math.DG

paper · pdf · doi:10.48550/arxiv.hep-th/9607133

37 pages, LateX2E+AMSLaTeX

openalex publication_date 1996/07/16 · arxiv created 1996/07/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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