On the quantum symmetry of rational field theories

TL;DR

This paper explores the role of Rational Hopf Algebras as symmetries in rational field theories, linking them with algebraic structures like braided categories and fusion rule algebras.

Contribution

It clarifies the connection between Rational Hopf Algebras and the algebraic structures underlying rational quantum field theories.

Findings

Rational Hopf Algebras serve as symmetry objects in rational field theories.

The paper establishes relations between Rational Hopf Algebras, braided monoidal categories, and fusion rule algebras.

It provides a framework connecting algebraic and categorical approaches to quantum field theory.

Abstract

We describe the role of Rational Hopf Algebras as the symmetries of rational field theories and discuss their relation with algebraic field theory, braided monoidal categories and modular fusion rule algebras.