Quantization Procedure

Quantum Field Theory · Part 2

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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. 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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