Decoherence of a composite system in QED and weak gravity

We study a spatial quantum superposition of a diatomic molecule type composite system and its decoherence due to emission of electromagnetic and gravitational radiation. The time-evolution of the reduced density matrix of the system with the influence functional from radiation fields is solved using the path integral formalism. It is shown that the spatial superposition state of a composite system can decohere by emission of radiation due to the fact that radiation is entangled with the internal degrees of freedom which is entangled with the external degrees of freedom. We also briefly discuss decoherence due to the quantization of the static Coulomb field generated by the superposed particle and the problems which arise when the electromagnetic field is replaced by gravity.