Physics:Quantum Electrodynamics (QED)

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

← Back to 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. 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.

Fields and particles

QED involves two fundamental fields:

• the electron (fermion) field $\psi (x)$
• the electromagnetic (gauge) field $A_{\mu }(x)$

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

Lagrangian of QED

The dynamics of QED are described by the Lagrangian: ${ℒ}=\overline{\psi }(i{\gamma }^{\mu }{D}_{\mu }-m)\psi -\frac{1}{4}{F}_{\mu \nu }{F}^{\mu \nu }$

where:

• $D_{\mu }={\partial }_{\mu }+ie{A}_{\mu }$ is the covariant derivative
• $F_{\mu \nu }$ is the electromagnetic field tensor
• $e$ is the electric charge

This structure encodes both free particle motion and their interaction.

Gauge symmetry

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

This symmetry requires the introduction of the gauge field $A_{\mu }(x)$, which mediates the electromagnetic interaction.

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.

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 $e$.

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.

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.

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.

Table of contents (175 articles)

Index

Core theory

1. Foundations
2. Conceptual and interpretations
3. Mathematical structure and systems
4. Atomic and spectroscopy
5. Wavefunctions and modes
6. Quantum dynamics and evolution
7. Measurement and information
8. Quantum information and computing

Matter (by scale)

9. Matter (by scale)

Applications and extensions

10. Quantum optics and experiments
11. Open quantum systems
12. Quantum field theory
13. Statistical mechanics and kinetic theory
14. Condensed matter and solid-state physics
15. Plasma and fusion physics
16. Timeline
17. Advanced and frontier topics

Methods and tools

18. Methods and tools

Full contents

1. Foundations (11)↑

1. Physics:Quantum basics
2. Physics:Quantum Postulates
3. Physics:Quantum Hilbert space
4. Physics:Quantum Observables and operators
5. Physics:Quantum mechanics
6. Physics:Quantum mechanics measurements
7. Physics:Quantum state
8. Physics:Quantum system
9. Physics:Quantum superposition
10. Physics:Quantum probability
11. Physics:Quantum Mathematical Foundations of Quantum Theory

2. Conceptual and interpretations (13)↑

12. Physics:Quantum Interpretations of quantum mechanics
13. Physics:Quantum Wave–particle duality
14. Physics:Quantum Complementarity principle
15. Physics:Quantum Uncertainty principle
16. Physics:Quantum Measurement problem
17. Physics:Quantum Bell's theorem
18. Physics:Quantum Hidden variable theory
19. Physics:Quantum nonlocality
20. Physics:Quantum contextuality
21. Physics:Quantum Darwinism
22. Physics:Quantum A Spooky Action at a Distance
23. Physics:Quantum A Walk Through the Universe
24. Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together

3. Mathematical structure and systems (13)↑

25. Physics:Quantum Density matrix
26. Physics:Quantum Exactly solvable quantum systems
27. Physics:Quantum Formulas Collection
28. Physics:Quantum A Matter Of Size
29. Physics:Quantum Symmetry in quantum mechanics
30. Physics:Quantum Angular momentum operator
31. Physics:Quantum Runge–Lenz vector
32. Physics:Quantum Approximation Methods
33. Physics:Quantum Matter Elements and Particles
34. Physics:Quantum Dirac equation
35. Physics:Quantum Klein–Gordon equation
36. Physics:Quantum pendulum
37. Physics:Quantum configuration space

4. Atomic and spectroscopy (14)↑

Quantum atomic structure and spectroscopy: orbitals, energy levels, and emission and absorption spectra.

38. Physics:Quantum Atomic structure and spectroscopy
39. Physics:Quantum Hydrogen atom
40. Physics:Quantum number
41. Physics:Quantum Multi-electron atoms
42. Physics:Quantum Fine structure
43. Physics:Quantum Hyperfine structure
44. Physics:Quantum Isotopic shift
45. Physics:Quantum defect
46. Physics:Quantum Zeeman effect
47. Physics:Quantum Stark effect
48. Physics:Quantum Spectral lines and series
49. Physics:Quantum Selection rules
50. Physics:Quantum Fermi's golden rule
51. Physics:Quantum beats

5. Wavefunctions and modes (9)↑

A quantum wavefunction showing probability amplitude in space; the square of its magnitude gives the probability density.

52. Physics:Quantum Wavefunction
53. Physics:Quantum Superposition principle
54. Physics:Quantum Eigenstates and eigenvalues
55. Physics:Quantum Boundary conditions and quantization
56. Physics:Quantum Standing waves and modes
57. Physics:Quantum Normal modes and field quantization
58. Physics:Number of independent spatial modes in a spherical volume
59. Physics:Quantum Density of states
60. Physics:Quantum carpet

6. Quantum dynamics and evolution (17)↑

61. Physics:Quantum Time evolution
62. Physics:Quantum Schrödinger equation
63. Physics:Quantum Time-dependent Schrödinger equation
64. Physics:Quantum Stationary states
65. Physics:Quantum Perturbation theory
66. Physics:Quantum Time-dependent perturbation theory
67. Physics:Quantum Adiabatic theorem
68. Physics:Quantum Scattering theory
69. Physics:Quantum S-matrix
70. Physics:Quantum tunnelling
71. Physics:Quantum speed limit
72. Physics:Quantum revival
73. Physics:Quantum reflection
74. Physics:Quantum oscillations
75. Physics:Quantum jump
76. Physics:Quantum boomerang effect
77. Physics:Quantum chaos

7. Measurement and information (8)↑

78. Physics:Quantum Measurement theory
79. Physics:Quantum Measurement operators
80. Physics:Quantum Projective measurement
81. Physics:Quantum POVM
82. Physics:Quantum Weak measurement
83. Physics:Quantum Measurement collapse
84. Physics:Quantum Zeno effect
85. Physics:Quantum limit

8. Quantum information and computing (10)↑

86. Physics:Quantum information theory
87. Physics:Quantum Qubit
88. Physics:Quantum Entanglement
89. Physics:Quantum Gates and circuits
90. Physics:Quantum Computing Algorithms in the NISQ Era
91. Physics:Quantum Noisy Qubits
92. Physics:Quantum random access code
93. Physics:Quantum pseudo-telepathy
94. Physics:Quantum network
95. Physics:Quantum money

9. Quantum optics and experiments (5)↑

Experimental quantum physics: qubits, dilution refrigerators, quantum communication, and laboratory systems.

96. Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy
97. Physics:Quantum optics beam splitter experiments
98. Physics:Quantum Ultra fast lasers
99. Physics:Quantum Experimental quantum physics
100. Physics:Quantum optics
Template:Quantum optics operators

10. Open quantum systems (9)↑

101. Physics:Quantum Open systems
102. Physics:Quantum Master equation
103. Physics:Quantum Lindblad equation
104. Physics:Quantum Decoherence
105. Physics:Quantum dissipation
106. Physics:Quantum Markov semigroup
107. Physics:Quantum Markovian dynamics
108. Physics:Quantum Non-Markovian dynamics
109. Physics:Quantum Trajectories

11. Quantum field theory (19)↑

Structural dependency map of quantum field theory.

110. Physics:Quantum field theory (QFT) basics
111. Physics:Quantum field theory (QFT) core
112. Physics:Quantum Fields and Particles
113. Physics:Quantum Second quantization
114. Physics:Quantum Harmonic Oscillator field modes
115. Physics:Quantum Creation and annihilation operators
116. Physics:Quantum vacuum fluctuations
117. Physics:Quantum Propagators in quantum field theory
118. Physics:Quantum Feynman diagrams
119. Physics:Quantum Path integral formulation
120. Physics:Quantum Renormalization in field theory
121. Physics:Quantum Renormalization group
122. Physics:Quantum Field Theory Gauge symmetry
123. Physics:Quantum Non-Abelian gauge theory
124. Physics:Quantum Electrodynamics (QED)
125. Physics:Quantum chromodynamics (QCD)
126. Physics:Quantum Electroweak theory
127. Physics:Quantum Standard Model
128. Physics:Quantum triviality

12. Statistical mechanics and kinetic theory (9)↑

129. Physics:Quantum Statistical mechanics
130. Physics:Quantum Partition function
131. Physics:Quantum Distribution functions
132. Physics:Quantum Liouville equation
133. Physics:Quantum Kinetic theory
134. Physics:Quantum Boltzmann equation
135. Physics:Quantum BBGKY hierarchy
136. Physics:Quantum Relaxation and thermalization
137. Physics:Quantum Thermodynamics

13. Condensed matter and solid-state physics (13)↑

138. Physics:Quantum Band structure
139. Physics:Quantum Fermi surfaces
140. Physics:Quantum Semiconductor physics
141. Physics:Quantum Phonons
142. Physics:Quantum Electron-phonon interaction
143. Physics:Quantum Superconductivity
144. Physics:Quantum Topological phases of matter
145. Physics:Quantum well
146. Physics:Quantum spin liquid
147. Physics:Quantum spin Hall effect
148. Physics:Quantum phase transition
149. Physics:Quantum critical point
150. Physics:Quantum dot

14. Plasma and fusion physics (8)↑

Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.

151. Physics:Quantum Fusion reactions and Lawson criterion
152. Physics:Quantum Plasma (fusion context)
153. Physics:Quantum Magnetic confinement fusion
154. Physics:Quantum Inertial confinement fusion
155. Physics:Quantum Plasma instabilities and turbulence
156. Physics:Quantum Tokamak core plasma
157. Physics:Quantum Tokamak edge physics and recycling asymmetries
158. Physics:Quantum Stellarator

15. Timeline (8)↑

159. Physics:Quantum mechanics/Timeline
160. Physics:Quantum mechanics/Timeline/Pre-quantum era
161. Physics:Quantum mechanics/Timeline/Old quantum theory
162. Physics:Quantum mechanics/Timeline/Modern quantum mechanics
163. Physics:Quantum mechanics/Timeline/Quantum field theory era
164. Physics:Quantum mechanics/Timeline/Quantum information era
165. Physics:Quantum mechanics/Timeline/Quantum technology era
166. Physics:Quantum mechanics/Timeline/Quiz

16. Advanced and frontier topics (8)↑

167. Physics:Quantum topology
168. Physics:Quantum battery
169. Physics:Quantum Supersymmetry
170. Physics:Quantum Black hole thermodynamics
171. Physics:Quantum Holographic principle
172. Physics:Quantum gravity
173. Physics:Quantum De Sitter invariant special relativity
174. Physics:Quantum Doubly special relativity

References

Author: Harold Foppele