The Dirac equation
eBook - ePub

The Dirac equation

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

The Dirac equation

About this book

This book is dedicated to the Dirac equation. The main arguments are: Dirac equation, gamma matrices in Dirac representation, properties of gamma matrices, covariance of the Dirac equation, Dirac Lagrangian and derivation of the Dirac equation from the equations of the Euler-Lagrange motion, Dirac equation in Hamiltonian form and free solutions in the rest and in any reference frame.

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Yes, you can access The Dirac equation by Alessio Mangoni in PDF and/or ePUB format, as well as other popular books in Physical Sciences & Quantum Theory. We have over one million books available in our catalogue for you to explore.

Information

Properties of the gamma matrices

We recall the fundamental relation that characterizes the Dirac gamma matrices, in particular the anti-commutator of any two gamma matrices is
image-72.png
from which, for example,
image-73.png
or, similarly,
image-74.png
The gamma matrices satisfy also the following relations
image-75.png
image-76.png
while the Hermitian conjugated of the gamma matrices are
image-77.png
with
image-78.png
from which
image-79.png
this means that the gamma matrices with spatial index are anti-hermitian, while
image-80.png
so that the gamma matr...

Table of contents

  1. Contents
  2. Introduction
  3. Notations
  4. Dirac equation
  5. Properties of the gamma matrices
  6. Covariance of the Dirac equation
  7. Dirac Hamiltonian
  8. Dirac Lagrangian
  9. Free solutions