Quantum electrodynamics

Quantum electrodynamics, or QED, is a quantum field theory of electromagnetism. QED describes all phenomena exhibited by charged point particles, such as electrons and positrons, and the particles of light (photons), interacting by electromagnetism. This theory includes classical electrodynamics in the limit of large fields, but also explains purely quantum phenomena such as the structure of atoms and molecules, the creation of particles by an electromagnetic field, and the anomalous magnetic moment of the electron. (The latter prediction has been experimentally confirmed to 11 decimal digits.)

QED was the first quantum field theory in which the difficulties of building a consistent, fully quantum description of fields and creation and annihilation of quantum particles were satisfactorily resolved. Sin-Itiro Tomonaga, Julian Schwinger, and Richard Feynman received the 1965 Nobel Prize in Physics for its development.

As QED is a gauge theory the starting point for its characteristic is its Lagrangian

${\displaystyle {\mathcal {L}}={\bar {\psi }}(i\gamma _{\mu }D^{\mu }-m)\psi -{\frac {1}{4}}F_{\mu \nu }F^{\mu \nu }}$

Here, ${\displaystyle \ \psi }$ and its Dirac adjoint ${\displaystyle {\bar {\psi }}}$ are the fields representing electrically charged particles, specifically electron and positron fields, represented as Dirac spinors. ${\displaystyle D_{\mu }=\partial _{\mu }+ieA_{\mu }}$ is the covariant derivative and ${\displaystyle e}$ is the coupling strength (which is the same as the elementary charge), ${\displaystyle A_{\mu }}$ the four-vector potential of the electromagnetic field and ${\displaystyle F_{\mu \nu }=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu }}$ is the electromagnetic field tensor (a ${\displaystyle 4\times 4}$ matrix combining the 3-vectors of the electric and magnetic field in a Lorentz covariant way.)

See sign convention.

See also Gauge theory, Functional integral.

Literature

R. P. Feynman, QED: The strange theory of light and matter [ISBN 0691024170]