# The Haag-Kastler Axioms for the $\mathscr{P}(\varphi)_2$ Model on the De Sitter Space

## TL;DR

This paper proves that the ${
m P}()_2$ quantum field theory model on two-dimensional de Sitter space satisfies the Haag-Kastler axioms, establishing a rigorous algebraic framework for this setting.

## Contribution

It extends the Haag-Kastler axioms to the ${
m P}()_2$ model on two-dimensional de Sitter space, providing a rigorous algebraic foundation.

## Key findings

- The ${
m P}()_2$ model on de Sitter space satisfies Haag-Kastler axioms.
- Provides a rigorous algebraic framework for quantum field theories on curved spacetime.
- Establishes foundational results for quantum fields in de Sitter geometry.

## Abstract

We establish the Haag-Kastler axioms for a class of models on the two-dimensional de Sitter space, including the ${\mathscr P} (\varphi)_2$ model.