A contribution to nonstandard superanalysis

The nonstandard (infinitesimal) analysis developed by Robinson is applied to certain foundational aspects of superanalysis. The construction of nonstandard hull due to Luxemburg is used to study ‘‘limit phenomena’’ arising in a Grassmann algebra Λ(q) as the number of generators q tends to infinity. An outcome of such an approach is that under transition t→∞ a superspace of purely odd dimension (0,q) transforms into a superspace of dimension (∞,∞) and not (0,∞) as one would expect. It is suggested that this construction may have something to do with the problem of adequate mathematical description of collective bosonic effects arising within infinite fermionic dimensions.