  Subject of this work are the applications of a field theoretical model,
called here generalized nonlinear sigma model or simply GNLSM,to the dynamics
of a chain subjected to constraints. Chains with similar properties and
constraints have been discussed in a seminal paper of Edwards and Goodyear
using an approach based on the Langevin equation. The GNLSM has been proposed
in a previous publication in order to describe the dynamics of a two
dimensional chain. In this paper the model is extended to d dimensions and a
bending energy term is added to its action. As an application, two observables
are computed in the case of a very stiff chain. The first observable is the
dynamical form factor of a ring shaped chain. The second observable is a
straightforward generalization to dynamics of the static form factor. This
observable is relevant in order to estimate the average distance between two
arbitrary points of the chain. Finally, a variant of the GNLNM is presented, in
which the topological conditions which constrain the motion of two linked
chains are imposed with the help of the Gauss linking invariant.
