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.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
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