# The Quantum Double of a Group and its relation to discrete gauge theories

Why is it that the algebraic structure known as the Quantum Double $D(G)$ of a discrete group is said to classify the excitations of a Discrete Gauge Theory (minimally coupled with matter) with gauge group $G$. My question arises because I am studying the so called Quantum Double models introduced by Kitaev. I understand the algebra of the operators that make the model is isomorphic to that of $D(G)$, what is not clear is the reason why the excitations are classified by the irreducible representations and the conjugacy classes of the quantum double $D(G)$. Any help would be greatly appreciated, also if anyone can give references where I can find some insights on the relation between the algebraic structure of $D(G)$ and Gauge Theories.

• Comment to the question (v1): Consider adding references in order to receive useful and focused answers. – Qmechanic Dec 18 '14 at 23:10