Spinors for Beginners 1: Introduction (Overview + Table of Contents for video series)
Why Physics Stack Exchange recommends it
Physics Stack Exchange answerers point people to it as a clear, beginner-friendly route into spinors, Clifford algebras, and the link between spin, helicity and chirality.
Recommended by 3 people across 3 different months, 2023 to 2024.
What it is
An 18-minute overview that opens eigenchris's 'Spinors for Beginners' series. It lays out a 'staircase' of topics, covering spinors as square roots of vectors, as members of Clifford algebras, via Lie groups and algebras, and in quantum field theory, with basic physics examples along the way.
What people said
Recommends naturallyInconsistent · 2023-07 · Physics Stack Exchange · on “How to arrive from a spin to a given polarization and what consequences does the solution imply?”
My understanding is that spins up and down are associated with left( $L$ ) and right( $R$ ) circular polarizations of a photon. Your idea is not completely wrong, but it is technically rather annoying to get this correct, and it should be known by more people than it currently is. There is no such thing as a usual spin for a photon. It does, however, have the projection of spin onto the momentum of a photon, and that is called helicity, and it is helicity that is corresponding to $\left|L\right>$ and $\left|R\right>$ . The most satisfactory treatment of spins and helicity (and chirality) together, lies in Wigner's work on the topic, and this is usually only done in QFT, which is a shame, bec
Recommends ramiel46692 · 2023-11 · Physics Stack Exchange · on “Understanding spinors, double cover and professor's expanation”
I know it is very unprofessional to give YouTube links, but these explanations are spot on, for a beginner: link [LINK] , link [this video] .
Recommends Léo Vacher · 2024-02 · Physics Stack Exchange · on “Spinor Components, Helicity, and Chirality in Dirac Theory”
I think that the clearest answer to your question has to be found in the mathematical formulation of spinors. $\frac{1}{2}(1\pm\gamma_5)$ acts as a projector operator allowing to obtain different irreducible representations of the Lorentz group. You will get a lot more intuition on its nature through the framework of Clifford algebra. For example you can have a look at this: [LINK] (and the discussion here [LINK] ) [this video] (especially lecture 13 for your question)