Narrow Results

In the present work the renormalized field theory for the Lagrangian formalism in terms of Hubbard operators is given. It is shown that starting from our path-integral representation found recently, it is possible to contruct the perturbative formalism and the standard Feynman diagram approach for operators verifying the Hubbard algebra. We show that by means of the introduction of proper ghost variables, propagators and vertices can be renormalized to each order. Our Lagrangian approach is checked using the Heisenberg ferromagnet and the antiferromagnet simpler models. In particular, the renormalized ferromagnetic magnon propagator coming from our formalism is studied in details, and it is shown how the softening of the magnon frequency is predicted by the model.

From the path-integral method, the diagrammatics and Feynman rules for the Lagrangian theory based on the spl(2,1) graded algebra are constructed. The first-order Lagrangian we have obtained is written in terms of the graded Hubbard operators. By using functional techniques, the correlation generating functional is given in terms of the proper effective Lagrangian of the model. Once the Feynman rules, propagators and vertices were found, a physical discussion about the free propagators is given. Finally, the expressions of the boson self-energy and the renormalized boson propagator are used to study the hole effects on the magnetic properties of the high-T_c cuprates.

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 decoupled representation.

The present work treats the role of ghost fields in the renormalization procedure of the Lagrangian perturbative formalism of the t–J model. We show that by introducing proper ghost field variables, the propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator coming from our previous Lagrangian formalism is studied in detail, and it is shown how the thermal softening of the magnon frequency is predicted by the model. The antiferromagnetic case is also analyzed, and the results are confronted with the previous one obtained by means of the spin-polaron theories.