Perturbation formalism of an exact representation for the t-J model

We show an exact representation of the t-J model by making use of a general Holstein-Primakoff transformation. The single occupancy constraint on the electrons is imposed strictly at every lattice site and the t-J Hamiltonian is transformed into an equivalent interacting boson and fermion system. The lowest-order approximation of a systematic perturbative expansion of the representation is shown to correspond to the mean-field theory of the Schwinger-boson approach. The second-order approximation gives the magnon-magnon, magnon-hole, and hole-hole interactions and the high-order antiferromagnetic spin polaron. In particular the second-order approximation takes further account of the renormalization of the magnon frequency and the antiferromagnetic spin polaron. The spectra of holes and magnons are calculated with the Green's function. The relevance of the obtained results to high-T-c superconductors is discussed.