The wave and field equations of this section are generalizations to unified field theory of the well-known wave and gauge field equations of electrodynamics [19]. Consider the Evans field equation in the form

G q^{a}_{μ} = kT q^{a}_{μ} .
(62)

The unified potential field is the tetrad or vector-valued one-form q^{a}_{μ} ,
which is in general an asymmetric square matrix. The latter can always
be written as the sum of symmetric and antisymmetric component
square matrices, components that are physically meaningful potential
fields of nature:

q^{a}_{μ} = q^{a}_{μ}^{(S)}
+ q^{a}_{μ}^{(A)} .
(63)

This decomposition is correct. However, it is useless because of not transforming covariantly.

and hence have NO PHYSICAL MEANING.

In the Evans unified field theory the gravitational potential field is
identified [1-10] as the tetrad q^{a}_{μ} and the electromagnetic
potential field
as A^{(o)}q^{a}_{μ} , where A^{(o)} is measured in volts.
The unit of magnetic flux,
i.e., the weber (or V ·s) belongs to h^{-}/e, the magnetic fluxon, and both h^{-}
and e are manifestations of the principle of least curvature [1-10] of the
Evans unified field theory. Both the gravitational and the electromagnetic
potential fields can in general have symmetric and antisymmetric components:

A^{a}_{μ} = A^{(o)} q^{a}_{μ} =
A^{a}_{μ}^{(S)}
+ A^{a}_{μ}^{(A)} ,
(64)

and hence have NO PHYSICAL MEANING.

and all four components appearing in Eqs. (63) and (64) are objectively
measurable fields of nature. Geometry shows that there can be two
types of gravitational potential fields: q^{a}_{μ}^{(S)}
and q^{a}_{μ}^{(A)} , and two types
of electromagnetic potential field, A^{a}_{μ}^{(S)} and
A^{a}_{μ}^{(A)}. These four types of
field are governed by four Evans field equations:

R_{1} q^{a}_{μ}^{(S)} =
− kT_{1} q^{a}_{μ}^{(S)} ,
(65)

R_{2} q^{a}_{μ}^{(A)} =
− kT_{2} q^{a}_{μ}^{(A)} ,
(66)

R_{3} A^{a}_{μ}^{(S)} =
− kT_{3} A^{a}_{μ}^{(S)} ,
(67)

R_{4} A^{a}_{μ}^{(A)} =
− kT_{4} A^{a}_{μ}^{(A)} ,
(68)

in which appear four types of canonical energy momentum tensor: symmetric
gravitational, antisymmetric gravitational, symmetric electromagnetic,
and antisymmetric electromagnetic.
. . .
We conclude that the symmetric part of the tetrad
q^{a}_{μ}^{(S)} represents the central, gravitational potential field, and the symmetric
A^{a}_{μ}^{(S)} represents the central, electrostatic potential field. The
antisymmetric A^{a}_{μ}^{(A)}
represents the rotating and translating electrodynamic potential field.

The antisymmetric q^{a}_{μ}^{(A)}
represents a type of spinning potential
field which is C positive, where C is charge conjugation symmetry
[20]. This fundamental potential field of nature is not present in the
Einsteinian or Newtonian theories of gravitation as argued and is a
field that is governed by the Evans equation (66). It may be the potential
field of dark matter [13], which is observed to constitute the
great majority of mass in the vicinity of spiral galaxies. Significantly,
the latter are thought to be formed by spinning motion, responsible
for their characteristic spiral shape. The field q^{a}_{μ}^{(A)}
is not centrally directed
and so does not manifest itself in the Newtonian inverse square
law in the weak-field limit. (Similarly, the antisymmetric electrodynamic
A^{a}_{μ}^{(A)}
µdoes not reduce to the Coulomb inverse square law, which
must be obtained [1-10] from the symmetric electrostatic A^{a}_{μ}^{(S)} .) The
antisymmetric q^{a}_{μ}^{(A)}
is also the root cause of the well-known Coriolis
and centripetal accelerations, which conventionally require a rotating
frame not present in Newtonian dynamics.

namely to q

. . .

All of these fields emerge systematically from the tetrad q^{a}_{μ} by
splitting it into its symmetric and antisymmetric components and by
multiplying them by a C negative coefficient whose unit is the volt.
The original asymmetric tetrad is the unified potential field of nature.
The C negative manifestation of the unified field is ζ^{(o)} q^{a}_{μ} ,
where ζ^{(o)}
must be determined experimentally. The coefficient ζ^{(o)} determines for
example the way in which an electrostatic field affects the gravitational
field. All forms of energy-momentum are interconvertible, implying
that

T^{a}_{μ} = T^{a}_{μ}^{(S)} +
T^{a}_{μ}^{(A)} .
(69)

A remark besides:

. . . the Cartan convention [11]

q^{a}_{μ} q^{μ}_{a} = 1,
(20)

The unspecified reference [11] is pointing to S.M. Carroll's Lecture Notes in General Relativity
where, of course, such nonsense cannot be found.

References

[1] M.W. Evans, New Concepts From The Evans Unified Field
Theory. Part One, **FoPL 18** p.139 ff.

http://www.aias.us/documents/uft/a12thpaper.pdf

[2] M.W. Evans, Chap. 14 of GENERALLY COVARIANT UNIFIED FIELD THEORY, Aramis 2005