The Renormalisation Group and Applications in Few-Body Physics

We study the distorted wave renormalisation group (DWRG), a tool for constructing power-counting schemes in systems where some diagrams must be summed to all orders. We solve the DWRG eqaution for a variety of long-range potentials including the Coulomb, Yukawa and inverse square. We derive established results in the case of the Yukawa and Coulomb potentials and new results in the case of the inverse square potential. We generalise the DWRG to systems of three-bodies and use it to find the power-counting for the three-body force in the KSW EFT. This power-counting corresponds to perturbations in the renormalisation group about a limit-cycle. We also derive equations for the LO and NLO KSW EFT distorted waves for three bosons and for three nucleons in the neutron-deuteron spin 1/2 channel. The physical results in the nuclear system agree well, once the LO three-body force is determined, with predictions of more sophistocated potential models.