Effective Lagrangians in bound state calculations (Q5938577)

Extended summary: In order to investigate specific aspects of bound state calculations in a non-relativistic framework, we consider the energy-levels of a massive scalar particle, which moves in an external field and interacts in addition with a massless scalar particle. The discussion includes the following topics: dimensionally regularized bound-state calculations, ultraviolet finiteness of bound-state observables and their independence of the off-mass-shell behavior of Green functions, non-renormalizable interactions, structure of the non-relativistic two-point function, power counting, and matching. Since detailed discussions of the renormalization program in the non-relativistic sector including explicit investigations of the two-point function seem not be available in the literature two respective examples are presented.