Kramers–Heisenberg formula Kramers–Heisenberg formula The Kramers–Heisenberg dispersion formula is an expression for the cross section for scattering of a photon by an atomic electron. It was derived before the advent of quantum mechanics by Hendrik Kramers and Werner Heisenberg in 1925, based on the correspondence principle applied to the classical dispersion formula for light. The quantum mechanical derivation was given by Paul Dirac in 1927. The Kramers–Heisenberg formula was an important achievement when it was published, explaining the notion of "negative absorption" (stimulated emission), the Thomas–Reiche–Kuhn sum rule, and inelastic scattering — where the energy of the scattered photon may be larger
Euler–Heisenberg Lagrangian Euler–Heisenberg Lagrangian In physics, the Euler–Heisenberg Lagrangian describes the non-linear dynamics of electromagnetic fields in vacuum. It was first obtained by Werner Heisenberg and Hans Heinrich Euler in 1936. By treating the vacuum as a medium, it predicts rates of quantum electrodynamics (QED) light interaction processes. It takes into account vacuum polarization to one loop, and is valid for electromagnetic fields that change slowly compared to the inverse electron mass: Here m is the electron mass, e the electron charge, formula_2, and formula_3. In the weak field limit, this becomes: formula_4 It describes photon-photon scattering in QED; Robert Karplus and