Functional integral approach in the theory of color superconductivity

In this series of lectures, we present the functional integral method for studying the superconducting pairing of quarks with the formation of diquarks, as well as the quark-antiquark pairing in dense QCD. The dynamical equations for the superconducting order parameters are the nonlinear integral equations for the composite quantum fields describing the quark-quark and quark-antiquark systems. These composite fields are bilocal fields if the pairing is generated by the gluon exchange, while for the instanton induced pairing interactions they are the local ones. The expressions of free energy densities are derived. The binding of three quarks is also discussed.