  Starting from a given topological invariant, we argue that it is possible to
construct a topological field theory with a finite number of Feynman diagrams
and an amplitude of gauge invariant objects that is a function of that
invariant. This is for example the case of the Gauss linking number and of the
abelian BF models which has been already successfully applied in the
statistical mechanics of polymers. In this work it is shown that a suitable
generalization of the BF model can be applied also to polymer dynamics, where
the polymer trajectories are not static, but change their shape during time.
