  We propose a new approach based on the path integral formalism to the
calculation of the probability distribution functions of quadratic quantities
of the Gaussian polymer chain in d-dimensional space, such as the radius of
gyration and potential energy in the parabolic well. In both cases we obtain
the exact relations for the characteristic function and cumulants. Using the
standard steepest-descent method, we evaluate the probability distribution
functions in two limiting cases of the large and small values of corresponding
variables.
