We introduce the coupling to an electromagnetic field to obtain an
interpretation of the internal structure of Dirac particles.
Consider the interaction of a point charge with an external
electromagnetic field.
The 4-potential is
, where
is a function
of
only.
We make the usual gauge invariant minimal substitution
![]() |
(5.20) |
where is the magnitude of the charge of an electron.
The Dirac equation becomes
![]() |
(5.21) |
or
![]() |
(5.22) |
This equation contains the interaction with the electromagnetic field:
![]() |
(5.23) |
where
![]() |
(5.24) |
and
![]() |
(5.25) |
is the classical correspondence of the relativistic velocity operator. We can see this by looking at the relativistic extension of the Ehrenfest relation:
![]() |
(5.26) |