Processes yielding high superconducting temperatures

It is pointed out that any microscopic description of the new high-$T_c$ superconductors should take into account a number of important points concerning strong couplings, whatever their nature: absence of the MacMillan limit, absence of a Migdal theorem, and importance of the Brovman-Kagan type of vertices with different singularities depending on the dimensionality. As a consequence, the applicability of standard techniques such as the Eliashberg theory, in particular, may be questioned in high-$T_c$ superconductors.