  The dynamics of a freely jointed chain in the continuous limit is described
by a field theory which closely resembles the nonlinear sigma model. The
generating functional $\Psi[J]$ of this field theory contains nonholonomic
constraints, which are imposed by inserting in the path integral expressing
$\Psi[J]$ a suitable product of delta functions. The same procedure is commonly
applied in statistical mechanics in order to enforce topological conditions on
a system of linked polymers. The disadvantage of this method is that the
contact with the stochastic process governing the diffusion of the chain is
apparently lost. The main goal of this work is to reestablish this contact. To
this purpose, it is shown here that the generating functional $\Psi[J]$
coincides with the generating functional of the correlation functions of the
solutions of a constrained Langevin equation. In the discrete case, this
Langevin equation describes as expected the Brownian motion of beads connected
together by links of fixed length.
