Effective action for local composite operators and dynamical symmetry breaking

In this paper a new formalism of effective action for local composite operators is proposed, in which the effective action is contributed by certain partially-two- particle-irreducible Feynman diagrams. This formalism is more convenient and effective than the conventional auxiliary field formalism in calculating complicated multi-field condensates. Some of its applications to two-dimensional field theories are given. Of special interest is the calculation of the non-factorized part of the four-fermion condensate left-angle bar ΨΨ bar ΨΨ right-angle beyond leading order in 1/N expansion