Learning the Simplicity of Scattering Amplitudes
This addresses a bottleneck in quantum field theory calculations for physicists by automating simplification tasks, though it is incremental as it builds on existing transformer architectures.
The paper tackles the problem of simplifying complex scattering amplitudes in theoretical high-energy physics using machine learning, achieving the ability to reduce expressions with hundreds of terms to vastly simpler equivalents, such as generating the Parke-Taylor formula for five-point gluon scattering and new compact expressions for other amplitudes.
The simplification and reorganization of complex expressions lies at the core of scientific progress, particularly in theoretical high-energy physics. This work explores the application of machine learning to a particular facet of this challenge: the task of simplifying scattering amplitudes expressed in terms of spinor-helicity variables. We demonstrate that an encoder-decoder transformer architecture achieves impressive simplification capabilities for expressions composed of handfuls of terms. Lengthier expressions are implemented in an additional embedding network, trained using contrastive learning, which isolates subexpressions that are more likely to simplify. The resulting framework is capable of reducing expressions with hundreds of terms - a regular occurrence in quantum field theory calculations - to vastly simpler equivalent expressions. Starting from lengthy input expressions, our networks can generate the Parke-Taylor formula for five-point gluon scattering, as well as new compact expressions for five-point amplitudes involving scalars and gravitons. An interactive demonstration can be found at https://spinorhelicity.streamlit.app .