Eur. Phys. J. C (2009) 60: 481-487
https://doi.org/10.1140/epjc/s10052-009-0922-5

Regular Article - Theoretical Physics

Faddeev–Jackiw canonical path integral quantization for a general scenario, its proper vertices and generating functionals

¹ Institute of Theoretical Physics, Beijing University of Technology, Beijing, 100022, China
² Institute of Physics, Chinese Academy of Sciences, Beijing, 100080, China
³ Institute of Modern Physics, Chinese Academy of Science, Lanzhou, 730000, China
⁴ CCAST (World Lab.), P.O. Box 8730, Beijing, 100080, China

^* e-mail: ychuang@bjut.edu.cn

Received: 5 January 2008
Revised: 17 January 2009
Published online: 20 February 2009

Abstract

We generalize the Faddeev–Jackiw canonical path integral quantization for the scenario of a Jacobian with J=1 to that for the general scenario of non-unit Jacobian, give the representation of the quantum transition amplitude with symplectic variables and obtain the generating functionals of the Green function and connected Green function. We deduce the unified expression of the symplectic field variable functions in terms of the Green function or the connected Green function with external sources. Furthermore, we generally get generating functionals of the general proper vertices of any n-points cases under the conditions of considering and not considering Grassmann variables, respectively; they are regular and are the simplest forms relative to the usual field theory.