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Effect of the Fermi surface reconstruction on the self-energy of the copper-oxide superconductors

We calculated the self-energy corrections beyond the mean-field solution of the rotating antiferromagnetism theory using the functional integral approach. The frequency dependence of the scattering rate ${1}/τ$ is evaluated for different temperatures and doping levels, and is compared with other approaches and with experiment. The general trends we found are fairly consistent with the extended Drude analysis of the optical conductivity, and with the nearly antiferromagnetic Fermi liquid as far as the ${\bf k}$-anisotropy is concerned and some aspects of the Marginal-Fermi liquid behavior. The present approach provides the justification from the microscopic point of view for the phenomenology of the marginal Fermi liquid ansatz, which was used in the calculation of several physical properties of the high-$T_C$ cuprates within the rotating antiferromagnetism theory. In addition, the expression of self-energy we calculated takes into account the two hot issues of the high-$T_C$ cuprate superconductors, namely the Fermi surface reconstruction and the hidden symmetry, which we believe are related to the pseudogap.