Quantization Procedure

Quantum Field Theory · Part 2

207 KB8 sections4 key equationsLaTeX typeset
Download PDFRead Online (Free)

Table of Contents

  1. 1.1.1 Review: Quantization in QM
  2. 2.1.2 Canonical Momentum for Fields
  3. 3.1.3 Equal-Time Canonical Commutation Relations
  4. 4.1.4 Hamiltonian Formulation
  5. 5.1.5 Heisenberg Equations of Motion
  6. 6.1.6 QM vs. QFT Quantization
  7. 7.Practice Problems
  8. 8.🎯 Key Takeaways

Key Equations

$$\pi(x,t) = \frac{\partial \mathcal{L}}{\partial(\partial_0\phi)} = \frac{\partial \mathcal{L}}{\partial \dot{\phi}}$$
$$\mathcal{H} = \pi\dot{\phi} - \mathcal{L}$$
$$\hat{H} = \int d^3x \, \mathcal{H}(\hat{\phi}, \hat{\pi})$$
$$\hat{H} = \int d^3x \left[\frac{1}{2}\hat{\pi}^2 + \frac{1}{2}(\nabla\hat{\phi})^2 + \frac{1}{2}m^2\hat{\phi}^2\right]$$

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,...

← Propagators
Spin Statistics →