# Braided quantum field theories and their symmetries

## TL;DR

This paper explores how braided quantum field theories, which incorporate Hopf algebra symmetries, can establish non-perturbative relations among correlation functions, with applications to noncommutative spacetimes.

## Contribution

It provides algebraic conditions linking Hopf algebra symmetries to braided quantum field theories and applies these to specific noncommutative models.

## Key findings

- Derived four algebraic conditions for symmetries in braided QFTs.
- Applied conditions to noncommutative field theories on Moyal plane and quantum gravity.
- Discussed implications for quantum field theory on kappa-Minkowski spacetime.

## Abstract

Braided quantum field theories proposed by Oeckl can provide a framework for defining quantum field theories having Hopf algebra symmetries. In quantum field theories, symmetries lead to non-perturbative relations among correlation functions. We discuss Hopf algebra symmetries and such relations in braided quantum field theories. We give the four algebraic conditions between Hopf algebra symmetries and braided quantum field theories, which are required for the relations to hold. As concrete examples, we apply our discussions to the Poincare symmetries of two examples of noncommutative field theories. One is the effective quantum field theory of three-dimensional quantum gravity coupled with spinless particles given by Freidel and Livine, and the other is noncommutative field theory on Moyal plane. We also comment on quantum field theory on kappa-Minkowski spacetime.