  In this work a method is presented to derive the generating functional in
path integral form for a system with an arbitrary number of degrees of freedom
and constrained by general conditions. The method is applied to the case of the
dynamics of an inextensible chain subjected to external forces. Next, the
generating functional of the inextensible chain is computed assuming that the
interactions are switched off. Finally, the generating functional of a two
dimensional nonlinear sigma model with O(3) symmetry is derived exploiting its
similarities with the model describing the dynamics of the inextensible chain.
