| quantum electrodynamics | |
|---|---|
| Name | Quantum electrodynamics |
| Caption | Example Feynman diagram for electron–electron scattering |
| Field | Quantum field theory |
| Introduced | 1940s |
| Notable figures | Richard Feynman; Julian Schwinger; Sin-Itiro Tomonaga; Freeman Dyson; Paul Dirac |
quantum electrodynamics
Quantum electrodynamics (QED) is the relativistic quantum field theory of the electromagnetic interaction, describing how charged particles interact by exchanging photons. It unifies classical electromagnetism and quantum mechanics within the framework of special relativity, providing extremely accurate predictions for phenomena at atomic and subatomic scales. QED is a cornerstone of quantum field theory and a prototype for other gauge theories such as quantum chromodynamics and the electroweak interaction.
QED grew from attempts to quantize the electromagnetic field and to reconcile the Dirac equation for the electron with radiative corrections. Early contributions include work by Paul Dirac on quantized fields and by Wolfgang Pauli on spin, but the modern covariant formulation was developed in the 1940s by Sin-Itiro Tomonaga, Julian Schwinger and Richard Feynman, with organizational synthesis by Freeman Dyson. Landmark results include the calculation of the Lamb shift in hydrogen and the anomalous magnetic moment of the electron, which validated QED against precision spectroscopy performed at institutions such as Harvard University and Bell Laboratories. QED's success influenced the formulation of the Standard Model and the development of renormalization theory by proponents like Kenneth Wilson and Gerard 't Hooft.
QED is a local, Lorentz-invariant gauge theory based on the abelian group U(1). The fundamental degrees of freedom are the Dirac spinor field ψ for charged fermions (e.g., electrons and positrons) and the vector potential Aμ for the photon. The classical action is expressed by the QED Lagrangian density: - kinetic terms for the fermion (Dirac Lagrangian) and the electromagnetic field (Maxwell Lagrangian), - a minimal coupling term ψ̄γμψ Aμ encoding charge conservation, - and gauge-fixing terms in covariant quantization schemes. This Lagrangian leads to equations of motion combining the Dirac equation and Maxwell's equations with quantum sources. Gauge symmetry implies the Ward–Takahashi identities, central to ensuring conservation of electric charge and the renormalizability demonstrated by Dyson and others.
Quantization of QED is typically performed via canonical quantization or path integral formulation techniques developed by Richard Feynman and others. The perturbative expansion organizes amplitudes into sums of Feynman diagrams, with external lines for asymptotic states (e.g., electrons, positrons, photons) and internal propagators for virtual particles. Key propagators include the fermion propagator (from the Dirac operator) and the photon propagator (from the Maxwell operator with gauge choice such as Feynman gauge). Interaction vertices carry factors of the elementary charge e and Dirac matrices γμ. Calculations of scattering amplitudes and bound-state corrections employ methods from the Bethe–Salpeter equation to nonrelativistic quantum electrodynamics (NRQED) for systematic expansions in the fine-structure constant α.
Loop diagrams in QED generate ultraviolet divergences requiring regularization and renormalization. Historic regularization methods included cutoff schemes and dimensional regularization introduced by Giambiagi and formalized in broader contexts by 't Hooft and Martinus Veltman. Renormalization absorbs infinities into redefinitions of mass, charge, and field normalization; physical predictions depend on renormalized parameters such as the running coupling α(μ). The renormalizability of QED was proven by Dyson and further clarified within the modern renormalization group framework advanced by Kenneth Wilson. Infrared divergences arising from soft photons are handled by the Bloch–Nordsieck theorem and the KLN theorem (Kinoshita–Lee–Nauenberg), ensuring cancellation in inclusive cross sections. Anomalies and gauge invariance considerations guide consistent extensions to non-abelian theories.
QED yields some of the most precise agreements between theory and experiment in physics. Prominent tests include: - the electron anomalous magnetic moment g−2, computed by high-order perturbation theory by teams including Toshihide Maskawa and measured by precision experiments at facilities like CERN and Brookhaven National Laboratory; - the Lamb shift measured in hydrogen spectroscopy at MIT and University of Paris laboratories; - radiative corrections to Bhabha scattering and Møller scattering tested in accelerator experiments at SLAC and DESY. Predictions require high-order loop integrals evaluated using techniques from perturbative quantum electrodynamics and numerical methods implemented in software such as FeynCalc and sector decomposition algorithms. Agreement between QED and experiment underpins the determination of fundamental constants like the fine-structure constant α and the electron mass.
QED methods extend to bound-state problems (e.g., positronium and hydrogenlike atoms) using non-relativistic QED (NRQED) and the Bethe logarithm for radiative corrections. Effective field theory approaches connect QED to low-energy phenomena and to the Standard Model Effective Field Theory (SMEFT). In condensed matter physics, emergent gauge fields and quasiparticles lead to analogues of QED: examples include graphene where charge carriers behave as relativistic Dirac fermions studied at University of Manchester; quantum electrodynamics in media describes phenomena like the Casimir effect measured by groups at Imperial College London and Bell Labs; and cavity quantum electrodynamics explores light–matter interaction in optical cavitys and circuit QED platforms developed in superconducting qubit research at institutions such as Yale University and Kavli Institute of Nanoscience. These extensions preserve core QED principles—gauge invariance, quantized fields, and perturbative techniques—while adapting to specific energy scales and many-body environments.
Category:Quantum electrodynamics Category:Quantum field theory