of the universe and a cluster of positrons on the other side of the universe. Because the theory is "sick" for any negative value of the coupling constant, the series does not converge but is at best an asymptotic series. From a modern perspective, we say that QED is not well defined as a quantum field theory to arbitrarily high energy. The coupling constant runs to infinity at finite energy, signalling a Landau pole. The problem is essentially that QED appears to suffer from quantum triviality issues. This is one of the motivations for embedding QED within a Grand Unified Theory. Electrodynamics in curved spacetime This theory can be extended, at least as a classical field theory, to curved spacetime. This arises similarly to the flat spacetime case, from coupling a free electromagnetic theory to a free fermion theory and including an interaction which promotes the partial derivative in the fermion theory to a gauge-covariant derivative. See also Abraham–Lorentz force Anomalous magnetic moment Bhabha scattering Cavity quantum electrodynamics Circuit quantum electrodynamics Compton scattering Euler–Heisenberg Lagrangian Gupta–Bleuler formalism Lamb shift Landau pole Moeller scattering Non-relativistic quantum electrodynamics Photon polarization Positronium Precision tests of QED QED vacuum QED: The Strange Theory of Light and Matter Quantization of the electromagnetic field Scalar electrodynamics Schrödinger equation Schwinger model Schwinger–Dyson equation Vacuum polarization Vertex function Wheeler–Feynman absorber theory References Further reading Books Journals External links Feynman's Nobel Prize lecture describing the evolution of QED and his role in it Feynman's New Zealand lectures on QED for non-physicists http://qed.wikina.org/ – Animations demonstrating QED Freeman Dyson Quantum electronics Quantum field theory