The electromagnetic dipole radiation field through the Hamiltonian approach

The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is discarded in the calculation of the radiation power. We believe that this simple case can elucidate some basic questions students pose when introduced to quantum electrodynamics or perturbation theory in quantum mechanics.