The quark-quark interaction in the nonrelativistic and in the lattice approximation

Abstract

The Galilean Hamiltonian for QCD is presented and illustrated. In a small quantization box such Hamiltonian exhibits a confining potential which, however, is a finite size effect, becoming purely Coulombic for infinite quantization volume. This does not necessarily imply absence of confinement in Galilean QCD, and a possible mechanism for confinement is discussed, suggested by the exact solution of the infrared sector in Galilean QED.

Finally the derivation of classical Galilean gauge theories and their quantization are sketched.