of the spectra makes one wonder if it can promote d-wave pairing. To investigate this, the momentum dependence of the coupling of the fermions to the fluctuations has been calculated. The coupling of the fermions to the fluctuations has been calculated [87]. In the contin- uum limit, U ( r ) is the angular momentum operator generating rotations of L ( r ). Therefore it can only couple to the local angular momentum of fermions. So the coupling is of the form H$_{int}$ has also been derived for the fermions in a two-dimensional model of the Cuprate lattice and the coupling constant g estimated in terms of the same microscopic model which gives the symmetry of the observed order and its approximate magnitude. It is useful to note that Eq. (39) is the natural orbital angular momentum analog of the familiar collective spin-fluctuation coupling to to spin-flip excitations of fermions. We may write Eq.(39) in momentum space; The coupling constant of the scattering of fermions to the fluctuation spectrum can be ex- tracted from the ARPES data in the normal state, Fig. (13) [86]. From such measurements, one deduces that the coupling constant λ$_{0}$ for all Cuprates measured by ARPES is between about 0 . 7and 1 and the cut-off ω$_{c}$ is between 0 . 4 eV and 0 . 5 eV. The lattice generalization of Eq. (40) also predicts that the scattering rate varies ∝ a + b cos(4 θ ) where θ is measured from the π, π direction with a variation of about a factor of 2 going from the π, π to the π, 0 direction. The momentum-dependence of coupling, even though the spectrum itself is momentum dependent is crucial to the symmetry of superconductivity promoted by the critical fluctu- ations. This is seen as follows: Integrating over the fluctuations in Eq.(40)gives an effective vertex for scattering of fermion-pairs: H$_{pairing}$ ≈ ∑ k σ k $^{′}$σ ′ Λ( k , k $^{′}$) c † σ ′ ( − k $^{′}$) c † $_{σ}$( k $^{′}$) c$_{σ}$ ( k ) c$_{σ}$ ′ ( − k ); Λ( k , k $^{′}$) = γ ( k, k $^{′}$) γ ( − k, − k $^{′}$)Re χ ( ω = ϵ$_{k}$ − ϵ $^{′}$$_{k}$) . (41) H$_{int}$ = ∑ k , k $^{′}$,σ gi ( ˆ k × ˆ k $^{′}$) ψ $^{+}$( k , σ ) ψ $^{+}$( k $^{′}$, σ ) U ( k − k $^{′}$) + H.C. (40) H$_{int}$ ∝ ∫ d r ∑ σ gψ $^{+}$( r , σ )( ˆr × ˆ p ) ψ ( r , σ ) U ( r ) + H.C. (39) 47