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{{Short description|Relativistic quantum field theory describing the interaction of charged particles with the electromagnetic field}}

{{Quantum book backlink|Quantum field theory}}
'''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.<ref name="peskin">Peskin, M. E.; Schroeder, D. V. ''An Introduction to Quantum Field Theory'' (1995).</ref> It is one of the most precisely tested theories in physics.

<div style="float:right; border:1px solid #ccc; padding:4px; background:#fff8dc; margin:0 0 1em 1em; width:420px;">
[[File:QED_interaction_diagram.jpg|400px]]
<div style="font-size:90%;">Electron–photon interaction in quantum electrodynamics represented by a Feynman diagram</div>
</div>

== 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.<ref name="weinberg">Weinberg, S. ''The Quantum Theory of Fields'' (1995).</ref>

== Fields and particles ==
QED involves two fundamental fields:

* the electron (fermion) field <math>\psi(x)</math>
* the electromagnetic (gauge) field <math>A_\mu(x)</math>

The photon is the quantum of the electromagnetic field, while electrons and positrons arise as excitations of the fermion field.<ref name="schwartz">Schwartz, M. D. ''Quantum Field Theory and the Standard Model'' (2014).</ref>

== Lagrangian of QED ==
The dynamics of QED are described by the Lagrangian:
<math>
\mathcal{L} = \bar{\psi}(i\gamma^\mu D_\mu - m)\psi - \frac{1}{4} F_{\mu\nu} F^{\mu\nu}
</math>

where:

* <math>D_\mu = \partial_\mu + ieA_\mu</math> is the covariant derivative
* <math>F_{\mu\nu}</math> is the electromagnetic field tensor
* <math>e</math> is the electric charge

This structure encodes both free particle motion and their interaction.<ref name="peskin"/>

== Gauge symmetry ==
QED is based on a local <math>U(1)</math> gauge symmetry. The theory remains invariant under transformations:
<math>
\psi(x) \rightarrow e^{i\alpha(x)} \psi(x)
</math>

This symmetry requires the introduction of the gauge field <math>A_\mu(x)</math>, which mediates the electromagnetic interaction.<ref name="weinberg"/>

== 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.<ref name="feynman">Feynman, R. P. (1949). Space-time approach to quantum electrodynamics.</ref>

== 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 <math>e</math>.<ref name="schwartz"/>

== 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.<ref name="zee">Zee, A. ''Quantum Field Theory in a Nutshell'' (2010).</ref>

== 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.<ref name="peskin"/>

== 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.

==See also==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

==References==
{{reflist|3}}
{{Author|Harold Foppele}}

{{Sourceattribution|Quantum field theory (QFT) core|1}}

Physics:Quantum Electrodynamics (QED) - Revision history

imported>WikiHarold: Repair Quantum Collection B backlink template

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