the conduction band is reflected in the existence of only one non-zero self-energy for the $f$-electrons. Nevertheless, it is useful to define an [*effective*]{} self-energy also for the conduction electrons as: This function describes the dressing of the $p$-electrons as an effect of both their hybridization with the correlated $f$-electrons and, indirectly, of the Hubbard repulsion on the latter. In particular, the appearance of a finite imaginary part in the zero-frequency limit signals the breakdown of a FL picture for the conduction electrons.

Since $\Sigma_{p \s}$ arises due to both the hybridization and the interaction $U$, it is not expected to vanish in the non-interacting limit $U=0$. On the other hand, it is easy to realize that in this limit the pure hybridization can not lead to a finite imaginary part of $\Sigma_{p \s}$ at zero frequency, and that any breakdown of the FL behavior can descend only from correlation effects.

DMFT equations {#sec1.2}
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The PAM has been studied using a large variety of numerical[@Grewe88; @Newns87; @Schweitzer91; @Fazekas87; @Pruschke00] and analytical methods.[@canionoce; @Gurin01; @Gulacsi02; @Shiba90] To access the non-perturbative regime of the PAM, we investigate the solution of the model using the DMFT, which has been used to solve 