  We evaluate several quantities appearing in the effective lagrangian for the
color-flavor locked phase of high density QCD using a formalism which exploits
the approximate decoupling of fermions with energy negative with respect to the
Fermi energy. The effective theory is essentially two-dimensional and exhibits
a Fermi velocity superselection rule, similar to the one found in the Heavy
Quark Effective Theory. Within the formalism we reproduce, using gradient
expansion, the results for the effective parameters of the Nambu-Goldstone
bosons. We also determine the dispersion laws for the gluons. By coupling the
theory to fermions and integrating over the two-dimensional degrees of freedom
we obtain the effective description of in-medium fermions.
