Mathematics

We discuss the Born-Oppenheimer approximation for two heavy particles interacting with a light particle via an attractive contact interaction in one dimension. The advantage of this simple model is that one can estimate the error terms self-consistently. Moreover, a Fock space approach to this problem is presented where a systematic expansion can be proposed to get higher order corrections. A slight modification of the same problem in which the light particle is relativistic is also discussed. The two dimensional version of the first case is more challenging due to renormalization issues, we propose a consistent approximation for this problem as well.