Geometric approach to a massive $p$ form duality

Massive theories of Abelian p forms are quantized in a generalized path representation that leads to a description of the phase space in terms of a pair of dual nonlocal operators analogous to the Wilson loop and the ’t Hooft disorder operators. Special attention is devoted to the study of the duality between the topologically massive and self-dual models in $2+1$ dimensions. It is shown that these models share a geometric representation in which just one nonlocal operator suffices to describe the observables.