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. 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,...

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