Scalar Fields

Quantum Field Theory · Part 1

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Table of Contents

  1. 1.3.1 Real Klein-Gordon Field
  2. 2.3.2 Plane Wave Solutions
  3. 3.3.3 Complex Scalar Field
  4. 4.3.4 U(1) Global Symmetry
  5. 5.3.5 Energy and Momentum for Scalar Fields
  6. 6.Equation of Motion
  7. 7.Dispersion Relation
  8. 8.General Solution
  9. 9.Equations of Motion
  10. 10.Infinitesimal Transformation

Key Equations

$$\mathcal{L} = \frac{1}{2}\partial_\mu \phi \partial^\mu \phi - \frac{1}{2}m^2 \phi^2 - V(\phi)$$
$$\boxed{p_\mu p^\mu = -E^2 + |\vec{p}|^2 = -m^2}$$
$$(\Box + m^2)\phi = 0, \quad (\Box + m^2)\phi^* = 0$$
$$\frac{\partial \mathcal{L}}{\partial(\partial_\mu \phi)} = \partial^\mu \phi^*, \quad \frac{\partial \mathcal{L}}{\partial(\partial_\mu \phi^*)} = \partial^\mu \phi$$

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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