Hamiltonian formalism for giant polaritons

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Abstract
We consider the interaction of a radiation field with excitons at high density, where the excitons cannot be approximated as bosons. In our approach, a dynamically equivalent Hamiltonian is constructed for relegating the nonboson commutation relations to boson commutation relations. For the self-consistent case, the ad hoc effective Hamiltonian can be made diagonal, yielding the eigenenergy of a giant polariton.