Derivation of the Gasser-Leutwyler Lagrangian from QCD

The normal part of the Gasser-Leutwyler formulation of the chiral Lagrangian is formally derived from the first principles of QCD without taking approximations. All the coefficients are expressed in terms of certain Green's functions in QCD, which can be regarded as the general QCD definitions of the normal part of the coefficients. The approximate values of the coefficients are also presented.