On a path integral having application in polymer physics

Using a path integral approach an explicit expression is obtained for the two-particle probability of a polymer chain for which both the elastic energy of stretching and the elastic energy of bending are taken into account. The end-to-end distribution function is extracted from this result. Points out that because of the elastic energy of bending the probability is non-Markoffian and, thus, in this case the two-particle probability is not identical in form to the end-to-end distribution. Moreover, when calculating averages over the length of the polymer it is necessary to use the two-particle probability rather than the end-to-end distribution. As an example the authors calculate the particle scattering factor for a dilute solution of polymers.