Dirac Field

Quantum Field Theory · Part 1

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Table of Contents

  1. 1.5.1 The Dirac Equation
  2. 2.5.2 Deriving the Dirac Equation
  3. 3.5.3 Dirac Adjoint and Conserved Current
  4. 4.5.4 Global U(1) Symmetry
  5. 5.5.5 Energy-Momentum Tensor for Dirac Field
  6. 6.📚 Related Topics
  7. 7.Gamma Matrices
  8. 8.Probability Current
  9. 9.Lorentz Invariance
  10. 10.Hamiltonian

Key Equations

$$\psi(x) = \begin{pmatrix} \psi_1(x) \\ \psi_2(x) \\ \psi_3(x) \\ \psi_4(x) \end{pmatrix}$$
$$-\gamma^\nu \gamma^\mu \partial_\nu \partial_\mu - m^2 = -\frac{1}{2}\{\gamma^\nu, \gamma^\mu\}\partial_\nu \partial_\mu - m^2 = -\partial_\mu \partial^\mu - m^2$$
$$j^0 = \psi^\dagger \psi \geq 0$$
$$\frac{\partial \mathcal{L}}{\partial(\partial_\mu \psi)} = i\bar{\psi}\gamma^\mu$$

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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