  In this work an approximated path integral model describing the dynamics of a
inextensible chain is presented. To this purpose, the nonlinear constraints
which enforce the property of inextensibility of the chain are relaxed and are
just imposed in an average sense. This strategy, which has been originally
proposed for semi-flexible polymers in statistical mechanics, is complicated in
the case of dynamics by the extra dependence on the time variable and by the
presence of nontrivial boundary conditions. Despite these complications, the
probability function of the chain, which measures the probability to pass to a
given initial conformation to a final one, is computed exactly. The Lagrange
multiplier imposing the relaxed condition satisfies a complicated nonlinear
equation, which has been solved assuming that the chain is very long.
