# Infrared finite scattering theory: Scattering states and representations of the BMS group

**Authors:** Kartik Prabhu, Gautam Satishchandran  
**arXiv:** [2402.00102](https://arxiv.org/abs/2402.00102)  
**Date:** 2024-01-31  
**Summary page:** https://www.summarizepaper.com/en/paper/2402.00102v1/

## Key points

- Kartik Prabhu and Gautam Satishchandran address infrared divergences in the standard S-matrix from non-trivial scattering with massless fields in four dimensions.
- They propose incorporating states with memory to achieve an infrared-finite scattering theory.
- The authors introduce direct-integral representations over the "Lorentz orbit" associated with a memory state.
- They classify all "orbit space representations" that have well-defined energy and angular momentum.
- The action of BMS charges on all states within this framework is explicitly outlined, emphasizing its importance in formulating an infrared-finite scattering theory.
- This methodology can be extended to obtain representations of the Poincaré group with memory for various quantum field theories.
- The study provides advancements in addressing infrared divergences in scattering processes involving massless fields by constructing physical states with memory.

## Summary

Kartik Prabhu and Gautam Satishchandran address the issue of infrared divergences in the standard S-matrix arising from non-trivial scattering involving massless fields in four spacetime dimensions. They propose incorporating states with memory into the formulation to achieve an infrared-finite scattering theory. The authors introduce direct-integral representations over the "Lorentz orbit" associated with a given memory state and classify all "orbit space representations" that possess well-defined energy and angular momentum. They explicitly outline the action of BMS charges on all states within this framework, highlighting its significance in formulating an infrared-finite scattering theory. Their methodology can be extended to obtain representations of the Poincaré group with memory for a broader range of quantum field theories. This study sheds light on crucial advancements in addressing infrared divergences in scattering processes involving massless fields, offering a concrete construction of physical states with memory and laying a foundation for developing more robust theoretical frameworks in quantum field theory.