Field correlator method for the confinement in QCD

The theory of confinement based on the stochastic field mechanism, known as the field correlator method (FCM) is discussed in detail. Experimental and lattice data have accumulated a vast amount of material on the properties of confinement in QCD. We enumerate all these properties as (1)-(7), and discuss beyond FCM two existing approaches: monopole based dual Ginzburg-Landau (DGL) theory, and Gribov-Zwanziger model, from this point of view. It is shown that the FCM satisfies all required criteria. We also prove its self-consistency; in particular, it is shown that the string tension sigma is the only scaleful parameter in the theory beyond fermion masses, and Lambda(QCD) is calculated explicitly to the lowest order in terms of sigma. We also formulate physical consequences of confinement, such as string breaking, Regge trajectories, role of confinement in the perturbation theory, chiral symmetry breaking, confinement in the boosted systems etc. It is demonstrated that the FCM is a suitable tool for the solution of these problems.