# Quantum Statistical Mechanics of the Absolute Galois Group

## TL;DR

This paper explores extending quantum statistical mechanics frameworks to non-abelian class field theory using the Galois group's action on dessins d'enfant, embedding in the Grothendieck-Teichmüller group, and the Drinfeld-Ihara involution.

## Contribution

It proposes a novel approach to non-abelian class field theory by integrating quantum statistical mechanics with Galois actions and related algebraic structures.

## Key findings

- Framework extensions for non-abelian class field theory
- Connections between Galois actions and quantum statistical models
- Potential insights into the structure of the absolute Galois group

## Abstract

We present possible extensions of the quantum statistical mechanical formulation of class field theory to the non-abelian case, based on the action of the absolute Galois group on Grothendieck's dessins d'enfant, the embedding in the Grothendieck-Teichm\"uller group, and the Drinfeld-Ihara involution.