Photon Quantization

Quantum Field Theory · Part 2

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Table of Contents

  1. 1.7.1 The Gauge Freedom Problem
  2. 2.7.2 Gauge Fixing Choices
  3. 3.7.3 Mode Expansion in Coulomb Gauge
  4. 4.7.4 Polarization Vectors
  5. 5.7.5 Canonical Commutation Relations
  6. 6.7.6 Hamiltonian and Photon States
  7. 7.7.7 Photon Propagator
  8. 8.7.8 Coupling to Matter: QED Lagrangian
  9. 9.7.9 Why Photons Are Massless
  10. 10.Practice Problems

Key Equations

$$\mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$$
$$\nabla \cdot \mathbf{A} = 0 \quad \text{and} \quad A^0 = 0$$
$$D_{\mu\nu}^F(x - y) = \langle 0 | T\{\hat{A}_\mu(x) \hat{A}_\nu(y)\} | 0 \rangle$$
$$\tilde{D}_{ij}^{\text{Coulomb}}(k) = \frac{-i}{k^2 + i\epsilon} \left(\delta_{ij} - \frac{k_i k_j}{|\mathbf{k}|^2}\right)$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Quantum Field Theory course on CoursesHub.World. Free online course in Quantum Field Theory (QFT). 8 parts covering classical field theory, canonical quantization, path integrals, QED, non-Abelian gauge theories, renormalization, the Standard Model,...

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