  A quantitative theory of the buckling of a worm like chain based on a
semi-classical approximation of the partition function is presented. The
contribution of thermal fluctuations to the force-extension relation that
allows to go beyond the classical Euler buckling is derived in the linear and
non-linear regime as well. It is shown that the thermal fluctuations in the
nonlinear buckling regime increase the end-to-end distance of the semiflexible
rod if it is confined to 2 dimensions as opposed to the 3 dimensional case. Our
approach allows a complete physical understanding of buckling in D=2 and in D=3
below and above the Euler transition.
