Effective Lagrangians and low energy photon-photon scattering
Abstract
We use the behavior of the photon-photon scattering for photon energies
ω
less than the electron mass,
m
e
, to examine the implications of treating the Euler-Heisenberg Lagrangian as an effective field theory. Specifically, we determine the
ω
2
/
m
2
e
behavior of the scattering amplitude predicted by including one-loop corrections to the Euler-Heisenberg effective Lagrangian together with the counterterms required by renomalizability. 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
ω
2
/
m
2
e
dependences of the two expansions differ.