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.
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Drew et al. (1997) studied this question.
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