(A) 00 = 0. Alternatively, to achieve the identical result, we could work in the coherent state basis , which shifts away a constant proportional to the identity in the electronic subspace from the Hamiltonian whereby, μ → μ -⟨µ⟩, with ⟨µ⟩ ≡ ⟨S 0 | μ|S 0 ⟩ is chosen to be the ground state permanent dipole moment. In both situations, the ground state is decoupled from the lightmatter interaction in the TC Hamiltonian, which is valid below the ultra-strong coupling regime where most experiments in linear spectroscopies of polaritons reside . In this case, the TC Hamiltonian, without the collective ground state |S 0 ⟩, which is to say,