  Amplitude fluctuations of the pairing field are responsible together with
phase fluctuations for the pseudogap phenomena in high temperature
superconductors. Here we present the more detailed theory of the amplitude and
phase fluctuations approach in the framework of a fermionic pairing model. New
experimental comparisons are presented for the specific heat of the curprate
LSCO confirming the generality of this phenomenological approach. The strong
decrease of amplitude fluctuations near optimal doping induces the illusion of
a "quantum critical point", which in fact does not exist since the pseudogap
energy scale is always different from zero even in the overdoped regime.
