Infinite-Dimensional Supermanifolds of Solutions in Lagrangian Field Theories with Fermion Fields

Abstract

Using the supergeometric interpretation of field functionals, we show that for quite a large 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. More precisely, we show that the smf of smooth Cauchy data with compact support is isomorphic with an smf of corresponding classical solutions of the model.