Nonlinear interaction between electromagnetic fields at high temperature

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The electron-positron `box' diagram produces an effective action which is fourth order in the electromagnetic field. We examine the behaviour of this effective action at high-temperature (in analytically continued imaginary-time thermal perturbation theory). We argue that there is a finite, nonzero limit as T→ ∞ (where T is the temperature). We calculate this limit in the nonrelativistic static case, and in the long-wavelength limit. We also briefly discuss the self-energy in 2-dimensional QED, which is similar in some respects.