Unique Structure of Free Particle Bound States

Free particle bound states - which exist only as microscopic systems - are discussed in quantum field theory assuming a QED like Lagrangian with fermion and boson fields. Due to a particular structure, severe boundary conditions can be defined related to geometry, momentum and energy-momentum conservation. Applied to hadrons and atoms, masses or binding energies as well as root mean square radii - which are different by many orders of magnitude between hadrons and atoms - are well described. The fulfillment of a total of about 10 boundary conditions (with three adjustable parameters only) can be considered as a unique and precise test of the mathematical structure of the underlying field theory.