Path integral quantization corresponding to Faddeev-Jackiw canonical quantization

Abstract

We analyze the structure of the Faddeev-Jackiw method and show that the canonical 2-form of the Lagrangian constructed in the last step of the Faddeev-Jackiw method is always nondegenerate. So according to the Darboux theorem, there must exist a coordinate transformation that can transform the Lagrangian into a standard form. We take the coordinates after the transformation as these in a phase space, and use this standard form of the Lagrangian, we achieve its path integral expression over the symplectic space, give the Faddeev-Jackiw canonical quantization of the path integral, and then we further show up the concrete application of the Faddeev-Jackiw canonical quantization of the path integral.