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

A simple replacement rule which allows the direct formulation in secon d quantization of the particle-photon interaction Hamiltonian in the v elocity gauge is presented. We show that a transformation of the creat ion and annihilation operators of the particle Hamiltonian gives the i nteraction Hamiltonian. The rule is valid for both local and nonlocal Hamiltonians and gives the correct expression of the photon self-inter action term A(2) also when only a projection of the particle Hamiltoni an is taken into account. As an example the replacement rule is applie d to the exciton operators in order to derive the polariton Hamiltonia n.