Front form QED(3+1): The spin-multiplet structure of the positronium spectrum at strong coupling

The practitioner has to think about (at least) two obstacles, when he wants to solve a Hamiltonian field theory problem in front form dynamics. One is the problem that the theory is not manifestly rotational invariant. The other is the question, how one should construct effective theories at all in this framework. Of course, the first problem exists analogously in instant form dynamics, where the theory is not manifestly Lorentz invariant. Connected to this problem is the fact that any symmetry which is not manifest will break down immediately with the slightest approximation in a Hamiltonian field theory. There is broad agreement that the construction of effective theories is inevitable, if one wants to describe the low energy region, i.e. the bound states, of a strongly coupled theory. A variety of formalisms were suggested concerning this topic [1][2][3].