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.

Mathematics

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.

Related Topics:
Abelian - Gauge theory - U(1) - Gauge group - Gauge field - Spin-1/2 - Field - Electromagnetic field

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The QED Lagrangian for the interaction of electrons and positrons through photons is

Related Topics:
Lagrangian - Electron - Positron - Photon

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:mathcal{L}=arpsi(igamma_mu D^mu-m)psi -rac{1}{4}F_{mu u}F^{mu u} .

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psi and its Dirac adjoint arpsi are the fields representing electrically charged particles, specifically electron and positron fields represented as Dirac spinors.

Related Topics:
Dirac adjoint - Fields - Charge - Electron - Positron - Dirac spinor

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D_mu = partial_mu+ieA_mu ,! is the gauge covariant derivative, with e the coupling strength (equal to the elementary charge), A_mu the covariant vector potential of the electromagnetic field and F_{mu u} = partial_mu A_ u - partial_ u A_mu ,! the electromagnetic field tensor. Also, gamma_mu are Dirac matrices.

Related Topics:
Gauge - Covariant - Derivative - Elementary charge - Vector potential - Electromagnetic field - Electromagnetic field tensor - Dirac matrices

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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.

Related Topics:
Electromagnetic field tensor - Electromagnetic field - Dirac-like equation - Gauge - Covariant - Derivative - Electron - Positron

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