Quantum Field Theory Course

Total: 440+ pages covering classical field theory through the Standard Model

Quantum Field Theory

Part IV: Interacting Field Theories

Applying the formalism: from simple toy models to Quantum Electrodynamics, the most precisely tested theory in physics.

Overview

Armed with canonical quantization (Part II) and path integrals (Part III), we're ready to compute real physics! Part IV applies these tools to interacting field theories: theories where particles actually scatter, decay, and create new particles.

We'll progress from simple scalar theories (φ⁴, Yukawa) to the crown jewel: Quantum Electrodynamics (QED) - the quantum theory of light and matter. QED predictions agree with experiment to 12 decimal places, making it the most precisely tested theory in all of science!

Course Structure

1. Interaction Picture & S-Matrix Theory

⚡

Deep dive into the interaction picture formalism. Time evolution with interactions, perturbative expansion, and systematic construction of S-matrix elements from Feynman diagrams.

S-matrix formalism • Dyson series • Wick's theorem in practice

2. Cross Sections & Decay Rates

📊

From amplitudes to observables! Computing differential cross sections, total cross sections, and decay rates. Phase space integrals, Mandelstam variables, and experimental signatures.

MIT Lecture 23 • dσ/dΩ • Decay width Γ • Phase space

3. Quantum Electrodynamics (QED)

⚛️

The quantum theory of electrons and photons. QED Lagrangian, gauge invariance, Feynman rules for QED, and the physical interpretation of virtual photons.

MIT Lecture 22 • ℒ = -¼FμνFμν + ψ̄(iγμDμ - m)ψ • Gauge theory

4. Elementary QED Processes I

e⁻γ

Classic QED processes at tree level: e⁺e⁻ annihilation, Compton scattering, pair production, and Bhabha scattering. Spin sums and traces of gamma matrices.

MIT Lecture 24 • e⁺e⁻ → μ⁺μ⁻ • Compton scattering • Spin averaging

5. Elementary QED Processes II

γγ

More complex QED processes: e⁻e⁻ scattering (Møller), photon-photon scattering, and three-body final states. Crossing symmetry and the power of Feynman diagrams.

MIT Lecture 25 • Møller scattering • γγ → e⁺e⁻ • Crossing

6. Radiative Corrections & Renormalization

∞→0

Beyond tree level: loop diagrams, virtual corrections, and the infinities they bring. Introduction to renormalization and how QED tames divergences to make finite predictions.

MIT Lecture 26 • Loop corrections • UV divergences • Renormalization preview

📚 Prerequisites

Before starting Part IV, you should have mastered:

🎯 What You'll Master

Computational Skills:

  • Computing S-matrix elements systematically
  • Calculating cross sections from amplitudes
  • Evaluating decay rates and lifetimes
  • Trace techniques for spin sums
  • Phase space integrals
  • Polarization sums for photons
  • One-loop calculations

Physical Insights:

  • QED as a gauge theory
  • Virtual particles and their effects
  • Crossing symmetry
  • Ward identities and gauge invariance
  • Origin of quantum corrections
  • Why renormalization is necessary
  • Connection to experimental results

🏆 QED: Triumph of Physics

Quantum Electrodynamics represents one of humanity's greatest intellectual achievements:

  • Anomalous magnetic moment of electron:
    Theory: ae = 0.001 159 652 181 78 (77)
    Experiment: ae = 0.001 159 652 180 73 (28)
    Agreement to 12 decimal places!
  • Lamb shift: Explained the 1057 MHz energy difference in hydrogen
  • Fine structure constant: α ≈ 1/137 measured to incredible precision
  • All atomic and molecular physics: Chemistry explained from first principles

"QED is the most precisely tested theory in all of science. It is also the jewel of physics – our proudest possession." - Richard Feynman

← Part III: Perturbation TheoryStart Part IV: Interaction Picture →