  Separation of the spin and orbital angular momenta of the electromagnetic
field has been discussed frequently in recent years. The spin and orbital
angular momenta cannot be made simultaneously gauge invariant and Lorentz
covariant and are not conserved separately. After analyzing the source of the
problem, we find that the electromagnetic 4-potential depends on the local
reference frame instead of the global reference frame. The transformation of
the local reference frame is the intrinsic degree of freedom of the
electromagnetic field. Therefore, considering only the Lorentz transformation
of the global reference frame and neglecting the Lorentz transformation of the
local reference frame may lead to the noncovariance of the electromagnetic
4-potential. Accordingly, we redescribe these difficulties of the
electromagnetic field from the perspective of quantum field theory. By using
the behavior of the electromagnetic 4-potential that satisfies the Coulomb
gauge in Lorentz coordinate transformation, we can construct the
electromagnetic vector in the tetrad bundle. The various physical quantities
that are induced by this electromagnetic vector satisfy Lorentz covariance in
the tetrad bundle. This electromagnetic vector, which is projected onto
space-time, is an electromagnetic 4-potential that satisfies the Coulomb gauge;
thus, the electromagnetic vector is gauge invariant.
