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We formally derive the chiral Lagrangian for low lying pseudoscalar mesonsfrom the first principles of QCD considering the contributions from the normalpart of the theory without taking approximations. The derivation is based onthe standard generating functional of QCD in the path integral formalism. Thegluon-field integration is formally carried out by expressing the result interms of physical Green's functions of the gluon. To integrate over thequark-field, we introduce a bilocal auxiliary field Phi(x,y) representing themesons. We then develop a consistent way of extracting the local pseudoscalardegree of freedom U(x) in Phi(x,y) and integrating out the rest degrees offreedom such that the complete pseudoscalar degree of freedom resides in U(x).With certain techniques, we work out the explicit U(x)-dependence of theeffective action up to the p^4-terms in the momentum expansion, which leads tothe desired chiral Lagrangian in which all the coefficients contributed fromthe normal part of the theory are expressed in terms of certain Green'sfunctions in QCD. Together with the existing QCD formulae for the anomalycontributions, the present results leads to the complete QCD definition of thecoefficients in the chiral Lagrangian. The relation between the present QCDdefinition of the p^2-order coefficient F_0^2 and the well-known approximateresult given by Pagels and Stokar is discussed.Comment: 16 pages in RevTex, some typos are corrected, version for publication  in Phys. Rev.

Derivation of the effective chiral Lagrangian for pseudoscalar mesons from QCD