Quantum Electrodynamics at strong Couplings

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 since the corresponding operators are complicated and involve the interaction. All approximations in solving Quantum Field Theories using front form dynamics, as inevitable as they are, are destined to destroy full Poincaré invariance. 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 α = 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 Jz 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 n. 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.