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In this work a method is presented to derive the generating functional inpath integral form for a system with an arbitrary number of degrees of freedomand constrained by general conditions. The method is applied to the case of thedynamics of an inextensible chain subjected to external forces. Next, thegenerating functional of the inextensible chain is computed assuming that theinteractions are switched off. Finally, the generating functional of a twodimensional nonlinear sigma model with O(3) symmetry is derived exploiting itssimilarities with the model describing the dynamics of the inextensible chain.

From constrained stochastic processes to the nonlinear sigma model. Two old problems revisited