  When metal becomes superconducting, new optical excitation channels are
created by particle-hole mixing. These excitation channels contribute
negligibly to optical responses in most superconductors, but they can be
relevant in ultra-strong-coupling superconductors that are close to the
Bose-Einstein condensate regime. Recently, selection rules for these
excitations have been formulated based on single-particle anti-unitary
symmetries in the mean-field theory. While being potentially useful for
studying optical properties of ultra-strong-coupling superconductors, they had
fundamental limitations because significant quantum fluctuations invalidate
mean-field approaches. Here, we use many-body states to formulate an optical
selection rule that does not rely on the mean-field approximation. In this
approach, the physical meaning of the previous selection rules becomes clearer
as they are simply recast as the selection rule for many-body inversion
eigenstates, not involving anti-unitary symmetries. This selection rule applies
not only to the Bogoliubov quasiparticles of Fermi liquids but also to
non-Fermi-liquid quasiparticles and electrically charged bosonic excitations.
We also study the Bogoliubov Fermi surfaces, whose topological stability is
closely related to the selection rule. We provide a many-body formulation of
their topological charges and show that the low-energy optical conductivity of
the Bogoliubov Fermi surfaces depends crucially on their secondary topological
charge. Finally, we discuss the implications of our results to the stability of
the superconducting state.
