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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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Book preview
The Dirac equation - Alessio Mangoni
2020
Contents
Contents
Introduction
Notations
Dirac equation
Properties of the gamma matrices
Covariance of the Dirac equation
Dirac Hamiltonian
Dirac Lagrangian
Free solutions
Introduction
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.
Notations
Generally we will use the Greek letters to indicate the indices that take values 0,1,2,3 and the Latin ones for the indices that assume values 1,2,3. Moreover we will use the Minkowski's metric tensor with signature (+,-,-,-), i.e.

and the Einstein summation convention that implies summation over two repeated indexes, one contravariant and one covariant, as for example,

Finally we will use the natural units, where

Dirac equation
The Dirac equation can be written, in natural units, in the form

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