In this video, we explore the mystery of spinors! What are these strange, surreal mathematical things? And what role do they play in physical reality? We'll talk about the algebra of SO(3) and SU(2), and the profound physical implications of spinors, particularly as it relates to spin-statistics and the stability of matter!
Video notes PDFs available for download on Patreon:
https://www.patreon.com/RichardBehiel
All support is highly motivating and greatly appreciated! :)
Recommended reading: "An introduction to spinors" by Andrew M. Steane: https://arxiv.org/abs/1312.3824
For a more advanced and comprehensive treatment of spinors, see "Spinors and Space-Time" by Penrose. The homotopy class animations in SO(3) were based on Section 1.5 of that book.
To learn more about the Spin-Statistics Theorem, see "Pauli and the Spin-Statistics Theorem", by Ian Duck and E. C. G. Sudarshan.
Also, check out the wonderful YouTube series "Spinors for Beginners" by EigenChris! https://www.youtube.com/@eigenchris
Chapters:
0:00 Intro
3:08 Topology Warmup
9:22 Axis-Angle Representation of 3D Rotations
13:15 Homotopy Classes of Loops in the Axis-Angle Space
22:50 The Algebra of Rotations, SO(N)
33:48 SU(2)
39:35 SU(2) Double Covers SO(3)
49:15 Exploring the Mystery
1:01:20 Superconductivity
1:05:00 Let's get Existential
1:07:50 Conclusion
#math #physiccs #quantum #quantumphysics #spinors
