Using the above expressions, the energy of the transverse fields, i.e., the last term in Eqn. B1 is quantized as follows This is commonly referred to as the "p • A" or the minimal coupling QED Hamiltonian, in the sense that the light and matter coupling is only carried through the matter momentum and the vector potential of the field. The minimal coupling structure in Eq. 4 comes naturally due to the local U (1) symmetry of the EM field, which is an Abelian gauge field.