Introduction to Spinor Calculus: Van der Waerden Notation

Based on "Physics from Symmetry" by Jacob Schwichtenberg ❤️
Timecodes:
00:00 - Intro
02:55 - Left and right spinors in VdW notation, and spinor conjugation as a way to convert between them
10:27 - Lorentz transforms of complex conjugated spinors
14:06 - Transposition as a way to combine two spinors in Lorenz invariant terms
17:45 - 4 types of spinor transforms: L, R, L† and R† († = complex conjugated and transposed)
20:37 - Why do we use transposition sign T in spinor notation explicitly?
23:07 - Lorentz transformations as rank-2 spinors
24:35 - Questions about the first part; spinors as a direct result of the spacetime symmetry
26:36 - What about other general relativity metrics? (I don't know the answer xD)
29:19 - Why Standard Model Lagrangian has the spinor indices hidden?
30:10 - Why do we need Dirac Spinors? A combination of 2 Weyl Spinors
31:20 - Invariant spinor terms to use in the Lagrangians - what are they in Weyl spinor terms?
31:43 - A way to convert between a 4 vector and 2-rank spinor (sl(2,c) Lie algebra)
33:18 - Invariant spinor terms with a spinor derivative (2-rank spinor encoded operator via sl(2,c))
34:10 - Why we're applying derivative only to one spinor? (answer: integration by parts gives us other possibility)
35:30 - Dirac matrices as a way to encode (1/2,0)+(0,1/2) rep: 2 Weyl spinors combination, and previous invariants in the Dirac notation (or Feynmann slash).
40:44 - Discussing popularity of the Dirac's encoding in university vs Weyl one directly. Dirac notation is confusing if you don't know the underlying principles and rep theory.
43:44 - spin 1/2 fields Lagrangian and Dirac Equations
45:22 - Plan for the next time
45:46 - (1/2, 1/2) rep, 4 vectors as 2-rank spinors
48:12 - Lorentz transformation of the 2-rank spinor and equivalence with 4-vector Lorentz transforms
52:27 - Spinors as "square roots" of 4-vectors (2-rank spinors, cause they have 2 spinorial indices)
54:50 - Other parts of Lorentz Group via CPT transforms
55:53 - Wrapping up the discussion. Questions
56:15 - Pauli vectors and adjoint representations: a way to convert vectors to spinorial objects
1:03:12 - Bosons and adjoint reps
I suggest you take a look at these videos by Eigenchris, before looking at the current one if you don't know about Lorenz Group representation theory:
• Spinors for Beginners ...
Please take a look at that playlist and the representation theory part of it.
You can also read Wiki article:
en.wikipedia.org/wiki/Represe...

[@karkunow]

00:00 - Intro 02:55 - Left and right spinors in VdW notation, and spinor conjugation as a way to convert between them 10:27 - Lorentz transforms of complex conjugated spinors 14:06 - Transposition as a way to combine two spinors in Lorenz invariant terms 17:45 - 4 types of spinor transforms: L, R, L† and R† († = complex conjugated and transposed) 20:37 - Why do we use transposition sign T in spinor notation explicitly? 23:07 - Lorentz transformations as rank-2 spinors 24:35 - Questions about the first part; spinors as a direct result of the spacetime symmetry 26:36 - What about other general relativity metrics? (I don't know the answer xD) 29:19 - Why Standard Model Lagrangian has the spinor indices hidden? 30:10 - Why do we need Dirac Spinors? A combination of 2 Weyl Spinors 31:20 - Invariant spinor terms to use in the Lagrangians - what are they in Weyl spinor terms? 31:43 - A way to convert between a 4 vector and 2-rank spinor (sl(2,c) Lie algebra) 33:18 - Invariant spinor terms with a spinor derivative (2-rank spinor encoded operator via sl(2,c)) 34:10 - Why we're applying derivative only to one spinor? (answer: integration by parts gives us other possibility) 35:30 - Dirac matrices as a way to encode (1/2,0)+(0,1/2) rep: 2 Weyl spinors combination, and previous invariants in the Dirac notation (or Feynmann slash). 40:44 - Discussing popularity of the Dirac's encoding in university vs Weyl one directly. Dirac notation is confusing if you don't know the underlying principles and rep theory. 43:44 - spin 1/2 fields Lagrangian and Dirac Equations 45:22 - Plan for the next time 45:46 - (1/2, 1/2) rep, 4 vectors as 2-rank spinors 48:12 - Lorentz transformation of the 2-rank spinor and equivalence with 4-vector Lorentz transforms 52:27 - Spinors as "square roots" of 4-vectors (2-rank spinors, cause they have 2 spinorial indices) 54:50 - Other parts of Lorentz Group via CPT transforms 55:53 - Wrapping up the discussion. Questions 56:15 - Pauli vectors and adjoint representations: a way to convert vectors to spinorial objects 1:03:12 - Bosons and adjoint reps