Dirac’s belt trick, Topology, and Spin ½ particles

ANSWERS TO FREQUENTLY ASKED QUESTIONS: This is my submission to 3Blue1Brown’s “Summer of Math Exposition 1“ #SoME1. In this video, I explain what Dirac’s famous belt trick has to do with the topology of rotating spin 1/2 particles, such as electrons. I created the 3D animations using , and the math animations with Manim Community . 00:00 Introduction 4:14 The space of rotations 9:40 Paths through the space of rotations 18:48 Group theory & the fundamental group 31:30 Quantum spin and SU(2) 39:31 SU(2) as the double cover of SO(3) 48:26 Bringing it all together 52:22 Tying up loose ends Music by Vincent Rubinetti Download the music on Bandcamp: Stream the music on Spotify: Largo From Concerto No 5