  Front form dynamics is not a manifestly rotational invariant formalism. In
particular, the requirement of an invariance under rotations around the
transverse axes is difficult to fulfill.In the present work it is investigated,
to which extent rotational invariance is restored in the solution of a
light-cone quantized field theory. The positronium spectrum in full (3+1)
dimensions is calculated at an unphysically large coupling of alpha=0.3 to be
sensitive for terms breaking rotational invariance and to accustomize the
theory to future QCD applications. The numerical accuracy of the formalism is
improved to allow for the calculation of mass eigenvalues for arbitrary
components J_z of the total angular momentum. We find numerically degenerate
eigenvalues as expected from rotationally invariant formalisms and the right
multiplet structures up to large principal quantum numbers. The results
indicate that rotational invariance is unproblematic even in front form
dynamics. Another focus of the work relies on the inclusion of the annihilation
channel. This enlargement of the model is non-trivial and a consistency check
of the underlying theory of effective interactions. The correct numerical
eigenvalue shifts, and especially the right hyperfine splitting are obtained.
Moreover, the cutoff dependence of the eigenvalues is improved drastically by
the annihilation channel for the triplet states. The implications of the
applied effective Hamiltonian approach are discussed in detail.
