Quantization of the non-Abelian Proca model based on the improved BFT formalism

We present the newly improved Batalin-Fradkin-Tyutin (BFT) Hamiltonian formalism and the generalization to the Lagrangian formulation, which pro= vide the more simple and transparent insight to the usual BFT method, with application to the non-Abelian Proca model which has been an difficult pr= oblem in the usual method. The infinite terms of the effectively first class constraints can be made to be the regular forms by ingenious choice of $X_{\alpha \beta}$ and $\omega^{\alpha \beta}$-matrices. In this new meth= od, the first class Hamiltonian, which also needs infinite correction terms i= s obtained simply by replacing the original variables in the original Hamil= tonian with the BFT physical variables. Remarkably all the infinite correction t= erms can be expressed the compact exponential form. We also show that in our m= odel the Poisson brackets of the BFT physical variables fields in the extended= phase space are the same structure as the Dirac brackets of the original phase = space variables. Based on our newly developed Lagrangian formulation we directl= y obtain that the desired gauge invariant Lagrangian including the non-Abel= ian Stückelberg scalar related to the explicit gauge symmetry breaking effe= ct due to the presence of the mass term without recourse to the path integral me= thod. The operator and path integral quantizations are also considered