  Extended particles are considered in terms of the fields on the Poincar\'{e}
group. Dirac like wave equations for extended particles of any spin are defined
on the various homogeneous spaces of the Poincar\'{e} group. Free fields of the
spin 1/2 and 1 (Dirac and Maxwell fields) are considered in detail on the
eight-dimensional homogeneous space, which is equivalent to a direct product of
Minkowski spacetime and two-dimensional complex sphere. It is shown that a
massless spin-1 field, corresponding to a photon field, should be defined
within principal series representations of the Lorentz group. Interaction
between spin-1/2 and spin-1 fields is studied in terms of a trilinear form. An
analogue of the Dyson formula for $S$-matrix is introduced on the
eight-dimensional homogeneous space. It is shown that in this case elements of
the $S$-matrix are defined by convergent integrals.
