A key difference between practical implementations of pQED and scQED resides in the treatment of the dipole self energy, specifically arising from the product of electronic operators in d e ˆ2. In the scQED approach, we are not starting with any specific state truncation in mind, and so our scQED Hamiltonian is written in terms of exact electronic operators. In first quantization, we can expand d e ˆ2 as