Positivity bounds on electromagnetic properties of media

I will talk about the constraints imposed on the electromagnetic response of general media by microcausality (commutators of local fields vanish outside the light cone) and positivity of the imaginary parts (the medium can only absorb energy from the external field). The effect of the medium is encoded in the electric and magnetic permeabilities ε(ω, k) and μ(ω, k). In the case of dielectrics, we obtain bounds on the low-energy values of the response, ε(0, 0) and μ(0, 0). In particular the quantities ε(0, 0) − 1 and ε(0, 0) − 1/μ(0, 0) are constrained to be positive and equal to integrals over the imaginary parts of the response.