Day 796: Fusion Rules and ε-Fermion

Learning Objectives

• •Define fusion rules for anyons and write the complete fusion table
• •Prove that $e \times e = 1$ and $m \times m = 1$
• •Derive the composite $\varepsilon = e \times m$ and its properties
• •Calculate the fermionic self-statistics of ε: $\theta_{\varepsilon\varepsilon} = \pi$
• •Verify the group structure $\mathcal{A} \cong \mathbb{Z}_2 \times \mathbb{Z}_2$
• •Connect fusion rules to the Verlinde formula

Today's Schedule (7 hours)