where Eq. 14 is a shift operator of the form Ûs = exp[iq 0 p/h] such that it shifts an arbitrary operator Ô(q) by an amount q 0 , Û † s Ô(q) Ûs = Ô(q -q 0 ). The polariton Hamiltonian under the Polarized Fock State (PFS) representation can then be written as