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. A comprehensive graduate-level course in quantum field theory. Covers classical field theory, canonical quantization, path integrals, gauge theories, renormalization, the Standard Model, and advanced ...

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