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

TL;DR

This paper develops an effective field theory for one-dimensional nonrelativistic particles with contact interactions, introducing velocity-dependent interactions, analyzing their renormalization group flow, and deriving the most general scattering amplitudes consistent with unitarity and time reversal.

Contribution

It introduces a new velocity-dependent contact interaction and provides a comprehensive analysis of its renormalization group behavior and scattering properties.

Findings

Identified a new velocity-dependent contact interaction.

Found a fixed point and a fixed line in the RG flow.

Derived the most general scattering amplitudes consistent with symmetries.

Abstract

We consider a field theory describing interacting nonrelativistic particles of two types, which map to each other under time reversal, with point-like interaction. We identify a new 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 point-like interaction consistent with unitarity and time reversal invariance.