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Quantum Field Theory · Part 2

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Table of Contents

  1. 1.2.1 Classical Solution: Plane Waves
  2. 2.2.2 Mode Expansion of Field Operator
  3. 3.2.3 Commutation Relations
  4. 4.2.4 Hamiltonian in Terms of Modes
  5. 5.2.5 Normal Ordering and Vacuum Energy
  6. 6.2.6 Particle States and Fock Space
  7. 7.2.7 Field Mode Visualization
  8. 8.2.8 Computational Example
  9. 9.🎯 Key Takeaways

Key Equations

$$\phi(x,t) = \int \frac{d^3k}{(2\pi)^3} \frac{1}{\sqrt{2\omega_k}} \left[a_k e^{-i(k \cdot x - \omega_k t)} + a_k^* e^{i(k \cdot x - \omega_k t)}\right]$$
$$\hat{\phi}(\mathbf{x},t) = \int \frac{d^3k}{(2\pi)^3} \frac{1}{\sqrt{2\omega_k}} \left[\hat{a}_k e^{i\mathbf{k} \cdot \mathbf{x}} e^{-i\omega_k t} + \hat{a}_k^\dagger e^{-i\mathbf{k} \cdot \mathbf{x}} e^{i\omega_k t}\right]$$
$$:\hat{H}: = \int \frac{d^3k}{(2\pi)^3} \omega_k \hat{a}_k^\dagger \hat{a}_k$$
$$|\mathbf{k}\rangle = \hat{a}_k^\dagger|0\rangle$$

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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