(Co)bordism groups in quantum super PDE's. II: Quantum super PDE's.

Following our previous works on the integral (co)bordism groups of quantum PDE's, we specialize, now, on quantum super partial differential equations, i.e., partial differential equations built in the category of {\em quantum supermanifolds}. These are manifolds modeled on locally convex topological vector spaces built starting from quantum algebras endowed also with a ${\mathbb Z}_2$-gradiation, and a ${\mathbb Z}_2$-graded Lie algebra structure, ({\em quantum superalgebra}). Then, we extend to these manifolds, with such richer structure, our previous results, and build a geometric theory of quantum super PDEs, that allows us to obtain theorems of existence of (smooth) local and global solutions in the category of quantum supermanifolds. Some quantum (super) PDE's, arising from the Dirac quantization of some classical (super) PDE's, are considered in some details.