Effective-field theory for one-dimensional nonrelativistic particles with contact interaction

Abstract

We consider a field theory describing interacting nonrelativistic particles of two types, which map to each other under time reversal, with pointlike interaction. We identify an alternative type of interaction which depends on the relative velocity between the particles. We compute the renormalization-group running of the coupling constants and find a fixed point and a fixed line. We show that the scattering amplitudes can be expressed in terms of three parameters. The result matches with a quantum-mechanical analysis and represents the most general pointlike interaction consistent with unitarity and time-reversal invariance.