NON-ABELIAN PROCA MODEL BASED ON THE IMPROVED BFT FORMALISM

Abstract

We present the newly improved Batalin–Fradkin–Tyutin (BFT) Hamiltonian formalism and the generalization to the Lagrangian formulation, which provide a much more simple and transparent insight into the usual BFT method, with application to the non-Abelian Proca model, which has been a difficult problem in the usual BFT method. The infinite terms of the effectively first class contraints can be made to be the regular power series forms by an ingenious choice of Xαβ and ωαβ matrices. In this new method, the first class Hamiltonian, which also needs infinite correction terms, is obtained simply by replacing the original variables in the original Hamiltonian with the BFT physical variables. Remarkably, all the infinite correction terms can be expressed in the compact exponential form. We also show that in our model the Poisson brackets of the BFT physical variables in the extended phase space have the same structure as the Dirac brackets of the original phase space variables. With the help of both our newly developed Lagrangian formulation and Hamilton's equations of motion, we obtain the desired classical Lagrangian corresponding to the first class Hamiltonian which can be reduced to the generalized Stückelberg Lagrangian which is a nontrivial conjecture in our infinitely many terms involved in the Hamiltonian and the Lagrangian.