Spinors

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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

https://www.youtube.com/watch?v=b7OIbMCIfs4&list=PLjH5ujQJt_IeW2qFkDRIBrZpIgx4ZX4AR&index=10&t=2882s

Spinors for Beginners

https://www.youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBs

Relació entre tensors i spinors (?)

D’alguna manera un escalar té spin 0 i un vector té spin 1 i un spinor té spin 1/2.

Té algo a veure amb el rang d’un tensor? o amb àlgebra geomètrica?

Doncs es veu que sí, veure minut 7:45 del següent vídeo. Diu spin 0 = escalar, spin 1 = vector i spin 2 = tensor de rang 2. És l’spin el rang??

Dubte

Aleshores un ‘camp’ (field) sempre és un camp tensorial, però que pot ser de rang enter o semienter i per tant tenim un camp escalar, un camp de spinors, un camp vectorial, un camp de spinors de 3/2, un camp de tensors de rang 2…?

El que pinta de moment

Tensor de rang 0 —> escalar

Tensor de rang 1/2 —> spinor (pseudovector?)

Tensor de rang 1 —> vector

Tensor de rang 2 —> tensor (de rang 2)

Tensor de rang 3/2 —> ? (pesudotensor de rang 2?)

Tensor de rang 3 —> tensor de rang 3

Subpàgines

Spinors (antic)

Spinors des de l’àlgebra geomètrica

YouTubePauli Spinors: Just Geometry, Not Quantum Magic!

Pauli Spinors: Just Geometry, Not Quantum Magic!

This video presents the idea that Pauli Spinors are the result of geometry rather than quantum mechanics, and that they have a simple and visualizable geometric interpretation! Invariant Decomposition & Spinors: https://arxiv.org/abs/2401.01142 My Last Video: https://www.youtube.com/watch?v=1uGKwVGeeJM My (Old & Gross) GA Playlist: https://www.youtube.com/playlist?list=PL4TOpi2EWY8a7dmFb7DbfPNKEAIZWi_rr Sudgy's Channel: https://www.youtube.com/@sudgylacmoe EigenChris' Channel: https://www.youtube.com/@eigenchris Bivector Discord Server: https://discord.com/invite/gdkFkEJuJM // Timestamps 00:00 - Intro & Foreword 01:47 - Summary of Geometric Algebra 06:33 - Plane Bisectors 09:24 - What Pauli Spinors Are 17:32 - Synopsis & Outro //Music Music by C418 Download the music on Bandcamp: https://c418.bandcamp.com/album/minecraft-volume-alpha Stream the music on Spotify: https://open.spotify.com/album/3Gt7rOjcZQoHCfnKl5AkK7 Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/playlist/3zNK20qC96mVSww60lVi1k #geometricalgebra #maths #mathematics #physics #geometry #spinor #spinors #spin #quantumphysics #quantummechanics