Copyright © 1999 David E. Rutherford
All Rights Reserved
We will now introduce the analogs of Maxwell's field equations and the Lorentz four-force equations. First, we will expand the analogs of Maxwell's field equations
We expand the first set of equations,
, to get
or
The second set of equations,
, obtained
by setting 
in Eqs. (69), is
The right-hand side of the last equality in Eqs. (71) can be reduced to one term by noting that
so that two of the terms cancel. The remaining term we interpret as
where the 
are the components of the current density four-vector. The relations for
the analogs of Maxwell's inhomogeneous equations now become
Inserting the components of
into Eqs.
(74), we have
where there is an additional implied sum over the repeated index,
. In addition
to the usual field terms of Maxwell's equations, we have, in Eqs. (75), the
terms, 
,
not found in Maxwell's equations. The
part of
, is the
trace of 
, as well as the four-divergence of the potential field. These terms imply
the existence of an extra induced current density
Copyright © 1999 David E. Rutherford
All Rights Reserved
E-mail: drutherford@softcom.net