Short description: Relativistic quantum field theory describing the interaction of charged particles with the electromagnetic field

Quantum electrodynamics (QED) is the quantum field theory of the electromagnetic interaction, describing how charged particles such as electrons interact with the electromagnetic field through the exchange of photons.^[1] It is one of the most precisely tested theories in physics.

Electron–photon interaction in quantum electrodynamics represented by a Feynman diagram

Basic idea

In QED, the electromagnetic field is quantized, and its excitations are photons. Charged particles interact by emitting and absorbing these photons.

This replaces the classical picture of continuous electromagnetic forces with a quantum description based on particle exchange.^[2]

Fields and particles

QED involves two fundamental fields:

the electron (fermion) field $ψ (x)$
the electromagnetic (gauge) field $A_{μ} (x)$

The photon is the quantum of the electromagnetic field, while electrons and positrons arise as excitations of the fermion field.^[3]

Lagrangian of QED

The dynamics of QED are described by the Lagrangian: $ℒ = \bar{ψ} (i γ^{μ} D_{μ} - m) ψ - \frac{1}{4} F_{μ ν} F^{μ ν}$

where:

$D_{μ} = \partial_{μ} + i e A_{μ}$ is the covariant derivative
$F_{μ ν}$ is the electromagnetic field tensor
$e$ is the electric charge

This structure encodes both free particle motion and their interaction.^[1]

Gauge symmetry

QED is based on a local $U (1)$ gauge symmetry. The theory remains invariant under transformations: $ψ (x) \to e^{i α (x)} ψ (x)$

This symmetry requires the introduction of the gauge field $A_{μ} (x)$ , which mediates the electromagnetic interaction.^[2]

Interaction mechanism

Interactions occur through the emission and absorption of photons. For example:

an electron emits a photon and changes momentum
a photon is absorbed by another charged particle

These processes are represented by Feynman diagrams and calculated using perturbation theory.^[4]

Propagators and vertices

In QED calculations:

electron lines correspond to fermion propagators
photon lines correspond to gauge boson propagators
interaction vertices connect one photon line with two fermion lines

Each vertex contributes a factor proportional to the coupling constant $e$ .^[3]

Precision and predictions

QED provides extremely accurate predictions, including:

the anomalous magnetic moment of the electron
the Lamb shift in atomic spectra
scattering cross sections in high-energy experiments

Agreement between theory and experiment reaches extraordinary precision.^[5]

Renormalization

QED contains divergences that arise in higher-order calculations. Renormalization absorbs these infinities into redefined physical parameters such as mass and charge.

This procedure yields finite, predictive results and was a major success of quantum field theory.^[1]

Conceptual importance

QED is the prototype of a successful quantum field theory. It demonstrates how:

gauge symmetry determines interactions
particles arise as field excitations
quantum corrections modify classical behavior

It forms the foundation for more complex theories such as the electroweak theory and the Standard Model.

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References

↑ ^1.0 ^1.1 ^1.2 Peskin, M. E.; Schroeder, D. V. An Introduction to Quantum Field Theory (1995).
↑ ^2.0 ^2.1 Weinberg, S. The Quantum Theory of Fields (1995).
↑ ^3.0 ^3.1 Schwartz, M. D. Quantum Field Theory and the Standard Model (2014).
↑ Feynman, R. P. (1949). Space-time approach to quantum electrodynamics.
↑ Zee, A. Quantum Field Theory in a Nutshell (2010).

Author: Harold Foppele

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[peskin-1] 1.0 ^1.1 ^1.2 Peskin, M. E.; Schroeder, D. V. An Introduction to Quantum Field Theory (1995).

[weinberg-2] 2.0 ^2.1 Weinberg, S. The Quantum Theory of Fields (1995).

[schwartz-3] 3.0 ^3.1 Schwartz, M. D. Quantum Field Theory and the Standard Model (2014).

[feynman-4] Feynman, R. P. (1949). Space-time approach to quantum electrodynamics.

[zee-5] Zee, A. Quantum Field Theory in a Nutshell (2010).

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Basic idea

Fields and particles

Lagrangian of QED

Gauge symmetry

Interaction mechanism

Propagators and vertices

Precision and predictions

Renormalization

Conceptual importance

See also

Table of content (86 articles)

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Physics:Quantum Electrodynamics (QED)

Basic idea

Fields and particles

Lagrangian of QED

Gauge symmetry

Interaction mechanism

Propagators and vertices

Precision and predictions

Renormalization

Conceptual importance

See also

Table of content (86 articles)

Core pathway

Full contents

References

Navigation

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