I mean that χ ”( q, ω, p, T ) integrated over all ω and k is χ$_{0}$ . The system of-course has other fluctuations but χ$_{0}$ saturates only part of the total spectral weight. The form (17) is suitable for discussing experiments as a function of ( p − p$_{c}$ ). For analyzing experiments as a function of frequency and temperature, an alternate form may be more useful: Thermodynamic and transport properties near a Gaussian qcp depend on the cut-off scale ω$_{c}$ , the spectral function χ$_{0}$ , the temperature T and the exponent z . The conventional theory of quantum criticality of ferromagnets gives z = 3 for ferromagnets and z = 2 for antiferromagnets. In this situation, the frequency scale as well as the momentum scale of the fluctuations → 0 as the critical point is approached just as near classical critical points; at a temperature T at p = p$_{c}$ , the frequency-scale of the fluctuation is T , and given in terms of ξ$_{t}$ by (20) away from it. Let us look at what such critical fluctuations do for T$_{c}$ through what we have just learnt in the previous section. In the quantum-critical regime, the scale of fluctuations just above T$_{c}$ or the cut-off scale in the fluctuations exchanged is T$_{c}$ itself. This is bad for two reasons: the prefactor of the expression for T$_{c}$ goes down with the cut-off, and as discussed and illustrated for ℓ = 0 pairing in Fig.(4), inelastic scattering has a particularly bad effect on T$_{c}$ . Is this compensated for by increase in the dimensionless coupling constants λ$_{ℓ}$ ? In other words does the peaking of fluctuation at low frequencies and in a region of width ξ − 1 r around the critical wave-vector increase the coupling constants. The answer is sadly, no. The point is that the coupling constant depends on the integrated value of the fluctuations over q and ω and these are essentially fixed by sum-rules. There is a weak (logarithmic) increase in the coupling constant if the spectra peaks at low frequencies which is generally quite uninteresting. Let us consider the role of χ$_{0}$ , the spectral weight. It may be taken from the ordered moment < M > far away from p$_{c}$ , where it is a slow function of p , to be ≈ < M > $^{2}$. This is a fraction ¯ χ$_{0}$ of the totals spectral weight of such fluctuations, the rest remaining as incoherent particle-hole fluctuations of fermions. As discuss below, the irreducible vertex is reduced by ¯ χ$_{0}$ compared with the case for phonons. In Sec. IV, we will review the firm experimental evidence for the case of the Cuprates and 24 χ ”( q, ω, p, T ) = χ$_{0}$T − d$_{M}$ $^{/z}$F 2 ( k T 1 $_{/z}$, ω T , 1 T ξ$_{t}$$^{)}$ . (20)