Generating particle physics Lagrangians with transformers

TL;DR

This paper demonstrates that transformer models can effectively generate particle physics Lagrangians, achieving high accuracy and understanding key physical concepts, thus aiding automated theoretical physics research.

Contribution

The authors trained a transformer to generate Lagrangians from particle lists, capturing gauge symmetries and internalizing physical concepts, a novel application in theoretical physics automation.

Findings

Achieved over 90% accuracy in Lagrangian prediction

Model generalizes beyond training data within constraints

Internalized group representations and conjugation concepts

Abstract

In physics, Lagrangians provide a systematic way to describe laws governing physical systems. In the context of particle physics, they encode the interactions and behavior of the fundamental building blocks of our universe. By treating Lagrangians as complex, rule-based constructs similar to linguistic expressions, we trained a transformer model -- proven to be effective in natural language tasks -- to predict the Lagrangian corresponding to a given list of particles. We report on the transformer's performance in constructing Lagrangians respecting the Standard Model $\mathrm{SU}(3)\times \mathrm{SU}(2)\times \mathrm{U}(1)$ gauge symmetries. The resulting model is shown to achieve high accuracies (over 90\%) with Lagrangians up to six matter fields, with the capacity to generalize beyond the training distribution, albeit within architectural constraints. We show through an analysis of input embeddings that the model has internalized concepts such as group representations and conjugation operations as it learned to generate Lagrangians. We make the model and training datasets available to the community. An interactive demonstration can be found at: \url{https://huggingface.co/spaces/JoseEliel/generate-lagrangians}.