Functional Renormalization Group Method And Dynamical Chiral Symmetry Breaking Of QCD

The content of this thesis, in the theoretical aspect concerns the functional renormalization group equation method, while in the physical phenomenal aspect it concerns dynamical chiral symmetry breaking and the conformal window of QCD.Renormalization is a very important concept in quantum field theory. And the functional renormalization group equation method (FRGE method) is an important part in the theory of renormaliztion. FRGE method has different formalisms, such Wilsonian formalism, Polchinski formalism and Wetterich for-malism. This thesis develops the Wetterich formalism FRGE method in two aspects.The Wetterich equation is dependent on the regulator, but a physical renor-malization equation should not be dependent on the regulator. This is the prob-lem of regulator. This thesis, through an investigation of the physical meaning of the regulator, introduces a parameter to control the suppression of the regulator, and solves this problem.The Wetterich equation is of one-loop form. If it is used directly and with simple approximations, then only one-loop results could be yielded. This thesis expands the Wetterich equation perturbatively, and introduces the concept of intermediate interaction. By doing this, this thesis proposes a convenient method to analyze some kinds of two-loop corrections.Dynamical chiral symmetry breaking and colour confinement are two im-portant infrared phenomena of QCD. In recent years, lattice calculations reveals that the critical fermion number of chiral symmetry is lesser than the critical fermion number of asymptotic freedom. This is contrary to the former belief that they are the same.This thesis calculates the renormalization flow equations through FRGE method, after investigating different flow patterns on the plane of dimensionless fermion mass and gauge coupling proposes the IR nontrivial fixed-point mecha-nism for nonoccurrence of dynamical chiral symmetry breaking. It says that if a theory is attracted to an IR nontrivial fixed-point in the finite region, then this theory will not show dynamical chiral symmetry breaking.The investigation of this thesis also reveals that when the fermion number is smaller than33/2, there can be also IR nontrivial fixed-point. So the existence of conformal window is also explained.