Dirac Quantization

Quantum Field Theory · Part 2

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Table of Contents

  1. 1.5.1 Review: Classical Dirac Field
  2. 2.5.2 Mode Expansion
  3. 3.5.3 Naive Quantization Fails!
  4. 4.5.4 The Solution: Anticommutators!
  5. 5.5.5 Pauli Exclusion Principle
  6. 6.5.6 Particles and Antiparticles
  7. 7.5.7 Equal-Time Anticommutation Relations
  8. 8.5.8 Dirac Propagator
  9. 9.5.9 Bosons vs. Fermions
  10. 10.Code Example: Dirac Spinor Modes

Key Equations

$$(i\gamma^\mu \partial_\mu - m)\psi = 0$$
$$\psi(x) = \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2E_p}} \sum_{s=1}^2 \left[ u^s(p) e^{-ip \cdot x} + v^s(p) e^{ip \cdot x} \right]$$
$$\hat{H} = \int \frac{d^3p}{(2\pi)^3} E_p \sum_s \left[ \hat{b}_p^{s\dagger}\hat{b}_p^s - \hat{d}_p^s\hat{d}_p^{s\dagger} \right]$$
$$n_p^s = \hat{b}_p^{s\dagger} \hat{b}_p^s, \quad n_p^s \in \{0, 1\}$$

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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