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 the 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 or quark-antiquark systems. These composite fields are the bi-local 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 the free energy densities are derived. The binding of three quarks is also discussed.Comment: 21 pages, 2 figures, Lectures at the VIth Vietnam International School in Theoretical Physics, Vung Tau, 27 December 1999 -- 08 January 200