Fractional Brownian motion models for polymers

Fractional Brownian motion (FBM) is a generalization of the usual Brownian motion. Recently we have given the correct path integral representation for it (K.L. Sebastian, J. Phys. A 28 (1995) 4305). Its measure shows that the process is Gaussian but is in general non-Markovian, even though Brownian motion itself is Markovian. We demonstrate this here by evaluating the three-point Greenʹs function. We point out certain uses and defects of the FBM as a model for polymer molecules.