Spinors for Beginners 9: Pauli Spinors vs Weyl Spinors vs Dirac Spinors

Review of Special Relativity

0:00 Intro / Overview
3:02 Special Relativity Review
4:43 Spacetime Interval
6:16 Lorentz Transformations SO(1,3)
10:12 Weyl Vectors
11:54 Double-Sided Lorentz SL(2,C)
17:45 Weyl Spinors Factoring
24:26 Spinor Inner Products
30:39 Left + Right Chirality
34:45 4 Types of Weyl Spinor (Van der Waerden notation)
43:06 Dirac Spinors
44:17 Conclusion / Review

[brightsideofmaths]

As a mathematical physicist, I really like this series. Please continue :)
Maybe, you are interested in a celebration livestream when we both reach the 100k subscribers? :) Could be fun!

[joefish]

about to take an exam on gauge theories and QFT been struggling to wrap my head around spinor fields and this video has came out almost perfectly timed, tysm !! :)

[lovi]

Framing the math in such a descriptive, visual, and story-like way is necessary for ensuring the physics is understood. Kudos kudos kudos!

[Wielorybkek]

I feel smarter and dumber at the same time after watching this video. what an experience.

[SamLoo-wn]

Keep going! These videos should be listed as references on any QFT syllabus.

[richardneifeld]

This was the most informationally dense video I have ever watched, and I understood every bit of it, thank you!

[lengooi]

Pauli, Weyl and Dirac would approve of this video ! Awesome and well done in explaining this in a clear and non confusing way.

[DrakeLarson-jspx]

This is a noteworthy Extreme Super-Synopsis of the exceptionally broad depth of nomenclature for spinors throughout the decades of physics. Congratulations to 'eigenchris' for this attempt ...VERY WELL DONE!...That said, spinor utilization should be exercised with care (and is undoubtedly subject to future modifications)...(Feynman had noteworthy comments about Dirac... and the same could be said for Pauli and Weyl, in a manner as Teller commented about Einstein's post 1919 attempts to advance physics.)

[boyastro]

The quick review of special relativity solidified my understanding of space-time in a big way! Thanks Chris.

[GustavoOliveira-gpnr]

I just found this series and I am addicted, it is in the perfrct pace and right to the point and very clear, thanks for creating this series!

[shivammahajan]

this is one of the most useful series i have found and is the chirality presented in this video related to the chirality in QFT is how and why (i am a big fan of your work)

[nice]

The part on the 4 different types of weyl spinors was very clear, I remember the headache when I first tried to understand them

[edd.]

Awesome video!!! Thank you so much for all the effort you put in to these videos. They are an incredible resource for my learning.

[BorisNVM]

i was using this in weyl spinors in the context of Supersymmetry and I had no idea where it came from. Cool video

[junghoonkwon]

It is definitely what I want to know about spin representation. thank for your video

[angeldude]

This looks like trying to do spacetime by representing time as a scalar rather than a vector. The Dirac spinors seem more appealing just because they put time on a more even footing with space.

In terms of Clifford Algebra, Weyl spinors and Pauli spinors both appear to use Cl(3), though Pauli spinors keep a firm distinction between the different grades while Weyl spinors don't. Dirac spinors appear to use Cl(1, 3) while keeping different grades distinct like the Pauli spinors.

[lame_lexem]

15:35 Note: it was quite upsetting that you used L for representing Weyl vector transformation matrices. if you used U insted we all would get the satisfying UWU†

[dariushimani]

This video was so good and helpful! Really helped me understand better. Looking forward to the next video in the series!

[just.a.guy]

Holy shit, when you started talking about Dirac spinors and it slowly became clear how antimatter is the time-reflection of matter because of the right dual Weyl spinors, that blew my mind! I feel like everything suddenly makes sense lol

[notwheeliesure]

What a woozie! We are obviously hitting the representational limits of symbols written on a 2D plane. It's so painfully obvious that the only thing making this material so obtuse is the notation. It's just the same simple concepts over and over again but we are forced to spend 99% of our brain power just deciphering the notation.