Effective Lagrangians and low energy photon-photon scattering

Abstract

We use the behavior of the photon-photon scattering for photon energies $\omega$ 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 ${\omega }^2/m_e^2$ 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 ${\omega }^2/m_e^2$ dependences of the two expansions differ.

10 pages, ReVTeX, 2 postscript figures included

References in corpus (1)

• Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals

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