  Space-time multivectors in Clifford algebra (space-time algebra) and their
application to nonlinear electrodynamics are considered. Functional product and
infinitesimal operators for translation and rotation groups are introduced,
where unit pseudoscalar or hyperimaginary unit is used instead of imaginary
unit. Basic systems of orthogonal functions (plane waves, cylindrical, and
spherical) for space-time multivectors are built by using the introduced
infinitesimal operators. Appropriate orthogonal decompositions for
electromagnetic field are presented. These decompositions are applied to
nonlinear electrodynamics. Appropriate first order equation systems for
cylindrical and spherical radial functions are obtained. Plane waves,
cylindrical, and spherical solutions to the linear electrodynamics are
represented by using the introduced orthogonal functions. A decomposition of a
plane wave in terms of the introduced spherical harmonics is obtained.
