Lattice QCD and nuclear physics

This chapter consists of three parts. In the first part, Lüscher's formula, which relates the scattering phase shift to the two particle energy in finite volume, is explained. A comprehensive but less rigorous derivation for the formula has been attempted for the ??-system as an example with emphasis on the Bethe-Salpeter (BS) wave function. In the second part, the BS wave function is considered to define the potential in quantum field theories. This method is applied to the two-nucleon system, in order to extract the NN -potential from lattice QCD. In the last part, the origin of the strong repulsion at short distance in the NN-potential, called the repulsive core, is theoretically investigated by the Operator Product Expansion and the renormalization group.