The Canonical Ward Identities In Constrained System And Their Application To The Dynamical Symmetry Breaking

The theory of constrained system is briefly reviewed. Dynamical symmetry breaking is expounded systematically. Cai~onica1 Ward-Takahashi identities with composite fields in the constrained system are proposed to investigate chiral symmetry dynamical breaking and gauge symmetry dynamical breaking.One basic feature in QCD is chiral symmetry and its spontaneousbreaking. Chiral o model and ENJL with SU(2)L x SU(2)R symmetry arediscussed, when electromagnetic field being considered, o , ~ and nucleon have different mass amendments. In chiral a model, ~ and nucleon have their mass through the chiral Ward-Takahashi method, which in agreement with the self-consistent method; for ENJL model, four antisymmetric tensor and four antisymmetric pseudotensor bosons exist which satisf~,?a mass relation previously derived for scalar and pseudoscalar meson from the 憈 Hooft interaction. Four-Fermion condense is discussed in the NJL model andderive mass spectrum of the four-fermion bound state, and what抯 more, the bound state contribute to mass of the fermion and the fermion-antifermion bound state.Finally, we discuss the dynamical symmetry breaking in the NonAbelian gauge theory. For pure Young-Mills theories, two vector meson composite field, three vector meson composite field and composite ghosts are constructed, and their mass spectrum are discussed. Where fermi field added to the pure Young-Mills theories, mass of fermion-antifermion bound state is derived, and it contribute to mass of vector meson and vector meson composite field.