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.
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