Composite particles within the Faddeev-Jackiw framework. Nonequivalence between the Dirac and Faddeev-Jackiw formalisms

Some time ago, the Faddeev-Jackiw canonical quantization formalism for constrained systems with Grassmann dynamical variables in the field theory context was reviewed. In the present work, the resulting formalism is applied to a classical nonrelativistic U(1) x U(1) gauge field model that describes the electromagnetic interaction of composite particles in 2 + 1 dimensions. The model contains a Chern-Simons U(1) field and the electromagnetic field, and it uses either a composite boson system or a composite fermion one. The obtained results are compared with the ones corresponding to the implementation of the Dirac formalism to this model, concluding that the Faddeev-Jackiw and Dirac methods cannot be considered equivalent. A simplified version of the above model is analyzed in the same way, similar to the one used within the framework of condensed matter. In this case, it is observed that when the results obtained by the Faddeev-Jackiw and Dirac methods coincide, the first method is more economical than the second one. For both models, the composite fermion case is explicitly considered.