Modified Faddeev–Jackiw quantization of massive non-Abelian Yang–Mills fields and Lagrange multiplier fields

Abstract

Massive Yang–Mills fields and Lagrange multiplier fields are quantized by the modified Faddeev–Jackiw quantization method, and the method's comparisons with Dirac method and the usual Faddeev–Jackiw method are also given. We show that this method not only is equivalent to Dirac method, but also remains all the virtues of the usual Faddeev–Jackiw method. Moreover, the modified Faddeev–Jackiw quantization method is simpler than the usual one when obtaining new secondary constraints. Therefore, the modified Faddeev–Jackiw method is more economical and effective than Dirac method and the usual Faddeev–Jackiw method. Meanwhile, we find the new meanings of the Lagrange multipliers, and discover that the Lagrange multipliers and the zeroth components of gauge field are just a pair of canonical field variables except a constant factor in this system.