We use the behavior of the photon-photon scattering for photon energies ω less than the electron mass, mₑ, to examine the implications of treating the Euler-Heisenberg Lagrangian as an effective field theory. Specifically, we determine the ω²/mₑ² behavior of the scattering amplitude predicted by including oneloop corrections to the Euler-Heisenberg effective Lagrangian together with the counterterms required by renormalizability. This behavior is compared with the energy dependence obtained by expanding the exact QED photon-photon scattering amplitude. If the introduction of counterterms in the effective field theory is restricted to those determined by renormalizability, the ω²/mₑ² dependences of the two expansions differ.
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Dicus et al. (1998) studied this question.
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