P-ADIC SUPERANALYSIS .2. SUPERMANIFOLDS AND DIFFERENTIAL-OPERATORS

This article is the second part of a work in which p-adic supermanifold theory is studied; by using the algebraic approach introduced in the first part of this work, p-adic superdifferential maps are introduced and, by restricting attention to the class of strictly differential maps, the foundation of p-adic supermanifold theory is developed herein. In particular it is shown that the superfield expansion theorem is no longer true: a superdifferential odd variables map which is not a polynomial is constructed. Finally, tangent space and Lie derivatives are constructed, and it is shown that no complex-valued fermion field of the p-adic argument could exist.