@Nagaosa-99] and then expand the action to quadratic (Gaussian) order in those fields. Although limited [@Haussmann-93; @Haussmann-94], such scheme suffices for the discussion of the BCS and BE limits. The novelty of our formulation is that pairs may be created and annihilated with different values of their angular momentum quantum numbers. In contrast, many previous applications of the Gaussian theory assumed these internal degrees of freedom of the Cooper pairs to be “frozen” to the desired $ s $ [@Zwerger-92; @SaDeMelo-Randeria-Engelbrecht-93] or $ d_{x^{2}-y^{2}} $ [@Zwerger-97] state. As we shall see these internal degrees of freedom turn out to be important, determining some of the key features of the problem. In sections \[SEC-gs\] and \[SEC-Tc\] we apply the formalism to discuss the ground state and the superconducting instability, respectively, in the BE limit, where the original argument for exotic pairing cannot be applied. Finally, in section \[SEC-conclusion\], we offer our conclusions.

Central potentials leading to exotic pairing\[SEC-central potentials leading to exotic pairing\]
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Let us begin by recalling some central ideas of the original weak-coupling theory of exotic pairing [@Balian-64; @Anderson-Brinkman-74]. Consider a system of electrons, in a three-dimensional continuum, interacting via some local, non-retarded, central potential $ V\left( \mathbf{r}-\mathbf{r}'\right) 