Quantum electrodynamics

'''Quantum electrodynamics''' ('''QED''') is a quantum field theory of electromagnetism. QED describes all phenomena involving electrically charged particles interacting by means of the electromagnetic force and has been called "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the muon, and the Lamb shift of the energy levels of hydrogen. Mathematically, QED has the structure of an Abelian gauge theory with a U(1) gauge group. The gauge field which mediates the interaction between the charged spin-1/2 fields is the electromagnetic field. Physically, this translates to the picture of charged particles (and their antiparticles) interacting with each other by the exchange of photons. These interactions can be described pictorially with Feynman diagrams, and QED was historically the theory to which Feynman diagrams were first applied. 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, their contributions involving a covariant and gauge invariant prescription for the calculation of observable quantities. Feynman's mathematical technique, based on his diagrams, initially seemed very different from the field-theoretic, operator-based approach of Schwinger and Tomonaga, but was later shown to be equivalent. The renormalization procedure for making sense of some of the infinite predictions of quantum field theory also found its first successful implementation in quantum electrodynamics. The QED Lagrangian for the interaction of electrons and positrons through photons is :$\backslash \backslash mathcal\{L\}=\backslash \backslash bar\backslash \backslash psi(i\backslash \backslash gamma\_\backslash \backslash mu\; D^\backslash \backslash mu-m)\backslash \backslash psi\; -\backslash \backslash frac\{1\}\{4\}F\_\{\backslash \backslash mu\backslash \; u\}F^\{\backslash \backslash mu\backslash \; u\}$ $\backslash \backslash \; \backslash \backslash psi$ and its Dirac adjoint $\backslash \backslash bar\backslash \backslash psi$ are the fields representing electrically charged particles, specifically electron and positron fields represented as Dirac spinors. $D\_\backslash \backslash mu\; =\; \backslash \backslash partial\_\backslash \backslash mu+ieA\_\backslash \backslash mu\; \backslash \backslash ,\backslash \backslash !$ is the gauge covariant derivative, with $\backslash \backslash \; e$ the coupling strength (equal to the elementary charge), $\backslash \backslash \; A\_\backslash \backslash mu$ the covariant vector potential of the electromagnetic field and $F\_\{\backslash \backslash mu\backslash \; u\}\; =\; \backslash \backslash partial\_\backslash \backslash mu\; A\_\backslash \; u\; -\; \backslash \backslash partial\_\backslash \; u\; A\_\backslash \backslash mu\; \backslash \backslash ,\backslash \backslash !$ the electromagnetic field tensor. Also, $\backslash \backslash gamma\_\backslash \backslash mu$ are Dirac matrices. The part of the Lagrangian containing the electromagnetic field tensor describes the free evolution of the electromagnetic field, whereas the Dirac-like equation with the gauge covariant derivative describes the free evolution of the electron and positron fields as well as their interaction with the electromagnetic field. The one-loop contribution to the [[vacuum polarization function Π]] The one-loop contribution to the electron self-energy function Σ The one-loop contribution to the vertex function Γ

See also

• Quantum field theory
• Gauge theory
• quantum gauge theory
• Gupta-Bleuler formalism
• vacuum polarization
• vertex function
• Renormalization
• Landau pole
• quantum chromodynamics
• Schwinger model
• Standard Model.

References

• R. P. Feynman, QED: The strange theory of light and matter [ Order: ISBN 0691024170]
• Claude Cohen-Tannoudji, Jacques Dupont-Roc, Gilbert Grynberg, Photons and Atoms : Introduction to Quantum Electrodynamics (John Wiley & Sons, 1997) [ Order: ISBN 0471184330]
• J. M. Jauch, F. Rohrlich, The Theory of Photons and Electrons (Springer-Verlag, 1980)
• R. P. Feynman, Quantum Electrodynamics (Perseus Publishing, 1998) [ Order: ISBN 0201360756]

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Classical mechanics

Condensed matter physics > Continuum mechanics

Electromagnetism > General relativity

Particle physics > Quantum field theory

Quantum mechanics > Solid state physics

Special relativity > Statistical mechanics

Thermodynamics

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