Quantum Electrodynamics is the relativistic quantum field theory describing electromagnetic interactions involving electrically charged matter and photons. It combines quantum mechanics with special relativity and quantises the electromagnetic field and charged matter fields. Electromagnetic interactions are mediated through the exchange and interaction of photons in the field-theoretic description. Quantum Electrodynamics is commonly abbreviated QED and is one of the most accurately tested theories in the history of Physics. It accounts for phenomena including the behaviour of electrons and positrons, photon scattering, electromagnetic radiation and extremely precise corrections to atomic energy levels and magnetic moments.
QED developed from the need to reconcile classical electromagnetism, quantum mechanics and special relativity. Early quantum theories of radiation encountered mathematical difficulties, while Dirac's relativistic electron equation provided a foundation for describing charged spin one-half particles and predicted antimatter. The modern renormalised formulation emerged through work by Julian Schwinger, Sin-Itiro Tomonaga, Richard Feynman and Freeman Dyson, who established mathematically equivalent approaches to calculating observable quantities. Their work transformed QED into a predictive quantum field theory capable of producing extremely precise agreement with experimental measurements.
The electromagnetic field is quantised in QED, with photons representing its quanta. Electrons and positrons are described by a relativistic fermionic field, while photons arise from the electromagnetic gauge field. The interaction between charged matter and the electromagnetic field is governed by the electric charge and the structure of the QED Lagrangian. Photons are massless gauge bosons with spin one, while electrons and positrons have spin one-half and nonzero rest mass. The theory therefore incorporates particle properties, field dynamics, relativity and quantum statistics within one consistent framework.
Feynman diagrams are widely used in QED calculations to represent terms in perturbative expansions of scattering amplitudes. A simple diagram may show an electron interacting with another charged particle through a photon line, but the diagram should not be interpreted as a literal microscopic photograph of what happens. It is a compact representation of mathematical terms. Internal lines correspond to propagator factors in the calculation and are often called virtual particles, but virtual particles are internal elements of perturbative calculations rather than directly observable particles travelling through space.
Renormalisation is essential to practical perturbative QED because naive calculations can contain divergent quantities. The theory reorganises these divergences so that measurable quantities such as physical charge and mass are related consistently to parameters appearing in the mathematical formulation. Renormalisation also reveals that effective electromagnetic coupling depends on energy scale. Vacuum polarisation contributes to this scale dependence, reflecting quantum fluctuations of charged fields. The running of the electromagnetic coupling is a central quantitative prediction of quantum field theory and has been tested through high-energy experiments and precision measurements.
QED predicts extremely precise physical effects. One famous example is the anomalous magnetic moment of the electron, whose measured value agrees with sophisticated theoretical calculations to remarkable precision. QED also predicts the Lamb shift, a small difference in atomic energy levels that is not fully accounted for by the simplest relativistic quantum treatment without radiative corrections. Other applications include photon scattering, electron positron interactions and radiative corrections to atomic and particle processes. These successes make QED a benchmark for testing quantum field theoretical methods.
QED has a gauge symmetry associated with the electromagnetic U one gauge group. Gauge invariance imposes strong mathematical constraints on the theory and is connected with charge conservation through the broader relationship between symmetries and conservation laws. The theory is Abelian, meaning that the electromagnetic gauge group has commuting generators, in contrast with non-Abelian gauge theories such as quantum chromodynamics. This distinction affects the mathematical structure of the fields and interactions. QED also forms part of the electroweak theory at higher energies, where electromagnetic and weak interactions arise from a larger gauge structure that is spontaneously broken to the familiar electromagnetic interaction.
QED should not be confused with classical electrodynamics. Maxwell's equations describe classical electromagnetic fields and remain highly accurate for many macroscopic situations, whereas QED describes quantum electromagnetic interactions and includes effects such as photon quantisation, vacuum polarisation and radiative corrections. QED itself is not a theory of gravity and is not intended to explain every fundamental interaction. Its scope is electromagnetic phenomena within a relativistic quantum framework. The exceptional agreement between QED calculations and experiments makes it one of the clearest demonstrations that quantum field theory can provide quantitatively precise descriptions of nature.
