Sum Rule for the Optical Hall Angle

We consider the optical Hall conductivity of a general electronic medium and prove that the optical Hall angle obeys a new sum rule. This sum rule governs the response of an electronic fluid to a Lorentz force and can be thought of as a counterpart to the $f$-sum rule in optical conductivity. The physical meaning of this sum rule is discussed, giving a number of examples of its application to a variety of electronic media.