Connection between the Slave-Particles and X-Operators Path-Integral   Representations. a New Perturbative Approach
  In the present work it is shown that the family of first-order Lagrangians for the t-J model and the corresponding correlation generating functional previously found can be exactly mapped into the slave-fermion decoupled representation. Next, by means of the Faddeev-Jackiw symplectic method, a different family of Lagrangians is constructed and it is shown how the corresponding correlation generating functional can be mapped into the slave-boson representation. Finally, in order to define the propagation of fermion modes we discuss two alternative ways to treat the fermionic sector in the path-integral formalism for the t-J model. 
A.Foussats, A. Greco, C.Repetto, O.P.Zandron and O.S.Zandron