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Quantum Electrodynamics

Quantum electrodynamics connects the interaction of charged matter with photons to scattering, magnetic moments and atomic spectra. This chapter develops representative calculations from the action through tree amplitudes, one-loop effects and nonrelativistic bound states. Along the way, distinguish a gauge-dependent intermediate quantity from a measurable result, and an auxiliary regulator from physical detector resolution.

Enter this chapter

Section titled “Enter this chapter”

Begin with The QED Action, Charges, and Observables to identify the fields, charge convention, and observables of the Abelian theory.

Topics

Section titled “Topics”
  1. The QED Action, Charges, and Observables — Defines the dynamical fields and physical observables.
  2. Tree-Level QED Processes — Builds amplitudes with consistent fermion signs and phase space.
  3. Renormalizing the Electron and Photon — Determines the field, mass, and charge counterterms.
  4. The Ward–Takahashi Identity and Charge Renormalization — Relates vertex and electron-propagator renormalization.
  5. Vacuum Polarization, Running Charge, and Screening — Connects photon polarization to charge screening and running.
  6. Soft Photons and Infrared-Finite QED — Combines unresolved radiation with virtual corrections.
  7. Lepton Magnetic Moments and the QED Form-Factor Expansion — Extracts magnetic moments from the on-shell vertex.
  8. Bound-State QED and NRQED — Separates atomic momentum, binding-energy, and hard scales.

How the ideas fit together

Section titled “How the ideas fit together”

The electron propagator and electromagnetic vertex cannot be renormalized independently: the Ward–Takahashi identity ties them together and constrains charge renormalization when the regulator and subtraction preserve the identity. This ultraviolet consistency still does not make an exclusive charged-particle amplitude infrared finite. Physical scattering also needs an inclusive radiation prescription, while bound states require a separate expansion in their momentum and binding scales. Thus the correct observable determines which cancellation or reorganization completes the calculation. Schwartz 2014, chs. 19–20.

Where to go next

Section titled “Where to go next”

Continue to Yang–Mills Theory to derive non-Abelian self-interactions from the field strength.

References

Section titled “References”
  • Schwartz, Matthew D. Quantum Field Theory and the Standard Model. Cambridge University Press, 2014. DOI.