In "introductory Quantum Optics", by Gerry and Knight, the Jeynes model is considered. In this model of electron-EM field interaction the electron is approximated by a two state system ($\lvert g\rangle$ and $\lvert e\rangle$), and the form of the dipole operator $\hat{d}$ is said to be constrained by parity consideration not to have on-diagonal terms:
Only the off-diagonal elements of the dipole operator are nonzero, since by parity consideration $\langle e\rvert\hat{d}\lvert e\rangle=0=\langle g\rvert\hat{d}\lvert g\rangle$.
Why? What does parity have to do with it?