Electromagnetic Field

Quantum Field Theory · Part 1

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Table of Contents

  1. 1.4.1 The Electromagnetic Lagrangian
  2. 2.4.2 The Field Strength Tensor
  3. 3.4.3 Maxwell's Equations from the Lagrangian
  4. 4.4.4 Gauge Invariance
  5. 5.4.5 Gauge Fixing
  6. 6.4.6 Classical vs. Quantum Electromagnetism
  7. 7.4.7 Coupling to Matter
  8. 8.📚 Supplementary Video Lectures
  9. 9.🎯 Key Takeaways

Key Equations

$$\mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$$
$$F^{\mu\nu} = \begin{pmatrix} 0 & -E_x & -E_y & -E_z \\ E_x & 0 & -B_z & B_y \\ E_y & B_z & 0 & -B_x \\ E_z & -B_y & B_x & 0 \end{pmatrix}$$
$$\partial_\mu F^{\mu\nu} = 0$$
$$\mathcal{L}_{\text{int}} = -j^\mu A_\mu = -(\rho A^0 - \mathbf{j} \cdot \mathbf{A})$$

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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