Extended Faddeev–Jackiw canonical quantization for the Podolsky electrodynamics

Abstract

We perform the Faddeev–Jackiw (FJ) canonical quantization for the Podolsky electrodynamics. To this end, we use an extension of the usual FJ formalism for constrained systems with Grassmann dynamical field variables, proposed by us some time ago. Besides, we compare the obtained results with those corresponding to the implementation of the Dirac formalism to this issue. In this way, we see that the extended FJ and the Dirac formalisms provide the same constraints and generalized brackets, thus suggesting the equivalence between these formalisms, at least for the present case. Furthermore, we find that the extended FJ formalism is more economical than the Dirac one as regards the calculation of both the constraints and the generalized brackets. On the other hand, we also compare the mentioned obtained results with the ones corresponding to the analysis of the issue in study by means of the usual FJ formalism, showing that between the extended and the usual FJ formalisms there are significant differences.