Differential structures on path spaces

We study general deformation structures on path spaces defined on manifolds and specialioze to those with memory. Furthermore, we highlight the construction of local operators on path space relatively compact to some position operator. The idea of this rather elementary work is to engage in the study of how perturbative string theory could be seen as a representation of a non commutative geometry. The latter, as studied in [1, 2] is acessible to direct physical interpretation.