Modeling the QCD ground state in the Hartree–Fock–Bogoliubov approximation

We study quark behavior in a strong stochastic gluon field. Based on the procedure of the averaged description, we derive the effective Hamiltonian and find its ground state in the Hartree–Fock–Bogoliubov approximation. We compare different model Hamiltonians. We discuss the chiral limit transition in detail in the example of the Keldysh model.