THE PARTICLE-PHOTON INTERACTION IN SYSTEMS DESCRIBED BY MODEL HAMILTONIANS IN 2ND QUANTIZATION

A simple replacement rule which allows the direct formulation in second quantization of the particle-photon interaction Hamiltonian in the velocity gauge is presented. We show that a transformation of the creation and annihilation operators of the particle Hamiltonian gives the interaction Hamiltonian. The rule is valid for both local and nonlocal Hamiltonians and gives the correct expression of the photon self-interaction term A(2) also when only a projection of the particle Hamiltonian is taken into account. As an example the replacement rule is applied to the exciton operators in order to derive the polariton Hamiltonian.