Quantum Electrodynamics -- from Eric Weisstein's World of Physics

Quantum electrodynamics is a generalization of quantum mechanics to include special relativity. Its governing equations are

It is even more difficult to solve problems exactly in quantum electrodynamics than it is in quantum mechanics. For example, in quantum electrodynamics, the gyromagnetic ratio of the electron has an infinite series of correction terms given in terms of the fine structure constant. These terms become increasingly difficult to calculate analytically (as they require evaluation of an increasingly large number of Feynman diagrams), but the first three are now known exactly.

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