  Dense relativistic matter has attracted a lot of attention over many decades
now, with a focus on an understanding of the phase structure and thermodynamics
of dense strong-interaction matter. The analysis of dense strong-interaction
matter is complicated by the fact that the system is expected to undergo a
transition from a regime governed by spontaneous chiral symmetry breaking at
low densities to a regime governed by the presence of a Cooper instability at
intermediate and high densities. Renormalization group (RG) approaches have
played and still play a prominent role in studies of dense matter in general.
In the present work, we study RG flows of dense relativistic systems in the
presence of a Cooper instability and analyze the role of the Silver-Blaze
property. In particular, we critically assess how to apply the derivative
expansion to study dense-matter systems in a systematic fashion. This also
involves a detailed discussion of regularization schemes. Guided by these
formal developments, we introduce a new class of regulator functions for
functional RG studies which is suitable to deal with the presence of a Cooper
instability in relativistic theories. We close by demonstrating its application
with the aid of a simple quark-diquark model.
