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The functional renormalization group equation is expanded to a two-loop form. This two-loop form equation involves one-loop effective action. An intermediate effective action perspective is adopted toward the one-loop effective action. That is to say, the intermediate effective action could not be of the same form of the bare action and one can make an ansatz to it. Thus by focusing on different high-dimensional operators, effects of the chosen operators can be investigated. QCD through intermediate 4-fermion interactions is investigated. Of the six kinds of 4-fermion interactions generated by one-loop QCD, four kinds generate fermion mass while the other two kinds decrease it. Flow patterns on the M²phys -- g² plane are drawn. [ABSTRACT FROM AUTHOR]

The dependence of functional renormalization group equation on regulators is investigated. A parameter is introduced to control the suppression of regulators. Functional renormalization group equations will become regulator-independent if this newly introduced parameter is sent to infinity in the end of calculation. One-loop renormalization flow equations of QCD are derived. The novelty is that both the coupling running equation and the mass running equation are mass-dependent. Different flow patterns are explored. A mechanism for nonoccurrence of dynamical chiral symmetry breaking is arrived at. The existence of a conformai window is also discussed in the language of renormalization flow. [ABSTRACT FROM AUTHOR]

The functional renormalization group equation is expanded to a two-loop form. This two-loop form equation involves one-loop effective action. An intermediate effective action perspective is adopted toward the one-loop effective action. That is to say, the intermediate effective action could not be of the same form of the bare action and one can make an ansatz to it. Thus by focusing on different high-dimensional operators, effects of the chosen operators can be investigated. QCD through intermediate 4-fermion interactions is investigated. Of the six kinds of 4-fermion interactions generated by one-loop QCD, four kinds generate fermion mass while the other two kinds decrease it. Flow patterns on the mphys²-g² plane are drawn. [ABSTRACT FROM AUTHOR]