On the structure of superfields in a field theory on a supermanifold

Abstract

In view of applications to the formulation of gauge field theories on supermanifolds, we study the relation between the sheaves of functions on a supermanifold M and its body manifold M0, respectively. The nonuniqueness of the local injections t: M0→M is analysed in consideration of its role in supersymmetric field theories. A Banach space structure is given to the set of bounded, supersmooth, Ckfields on M in order to get a rigorous formulation of variational principles for the class of theories under consideration.