Chiral Effective Lagrangian With ?(1232)

Chiral perturbation theory(ChPT)is used to study the low energy hadron physics according to the chiral symmetry by taking the light quark masses to zero.The first step in the chiral perturbation theory is to get the chiral Lagrangian.The lower order effective Lagrangians of pseudoscalar mesons and baryons have already been constructed.The lowest excited states of the nucleon are the four ?(1232)baryons.Chiral perturbative the-ory gives an effective implementation to describe ?(1232),evading the non-perturbative effects of QCD.Tnere are many ways to describe the spin-3/2 fields.The vector-spinor representation is the best one in presenting their interaction forms,which is important in the quantum field theory,es-pecially in Chiral perturbative theory.We will adopt this widely used vector-spinor representation(Rarita-Schwinger field)to give the Lagrangian with ?(1232).In this thesis,we would like to construct the chiral Lagrangians with ?(1232)up to the one-loop level by considering various constraints.For example,the point transform of Rarita-Schwinger field and the constraint relation in isovector-isospinor space,Schouten identity,Partial integration,Equations of motion,Bianchi identity and so on.Adopting a systematic approach and using symbolic computation method,we get the 0(p4)?(1232)Lagrangian.For the ??? La-grangian,one obtains 38 independent terms at the order 0(p3)and 318 independent terms at the order O(p4).For the ?N? Lagrangian,we get 33 independent terms at the order 0(p3)and 218 independent terms at the order O(p4).