1. ### I Lorentz transformation of the "bilinear spinor matrixelement"

Dear reader, there is a physics problem where I couldn't understand what the solutions. It is about the lorentz transformation of a bilinear spinor matrix element thing. So the blue colored equation signs are the parts which I couldn't figure out how. There must be some steps in between which...
2. ### A Gamma - traceless

I read this question https://physics.stackexchange.com/questions/95970/under-what-conditions-is-a-vector-spinor-gamma-trace-free . Also I read Sexl and Urbantke book about groups. But I dont understand why spinors is irreducible if these are gamma-tracelees. Also I read many papers about higher...
3. ### I Chirality projection operator

Hello everybody! I have a doubt in using the chiral projection operators. In principle, it should be ##P_L \psi = \psi_L##. $$P_L = \frac{1-\gamma^5}{2} = \frac{1}{2} \begin{pmatrix} \mathbb{I} & -\mathbb{I} \\ -\mathbb{I} & \mathbb{I} \end{pmatrix}$$ If I consider ##\psi = \begin{pmatrix}...

10. B

### Dual spinor and gamma matrices

Here it is a simple problem which is giving me an headache, Recall from class that in order to build an invariant out of spinors we had to introduce a somewhat unexpected form for the dual spinor, i.e. ߰ψ = ψ†⋅γ0 Then showing that ߰ is invariant depends on the result that (ei/4⋅σμν⋅ωμν)† ⋅γ0...
11. ### Massive spin-s representations of the Poincare group

Context The following is from the book "Ideas and methods in supersymmetry and supergravity" by I.L. Buchbinder and S.M Kuzenko, pg 56-60. It is about realizing the irreducible massive representations of the Poincare group as spin tensor fields which transform under certain representations of...
12. ### I What is a spinor?

Okay, I have read on spinors here and there but I really don't understand geometrically or intuitively what it is. Can someone please explain it to me and how/when it is used? Thanks!
13. ### I What kind of space is the space of spinors?

Hi, i dont find much about spinor spaces. I can think in that spaces like a vector space above the field of complex numbers (a complex vector space)? sorry if what i saying is a non-sense, but i really want to understand better the math behind the concept of a spinor. thanks
14. ### System of ODE - comparison with paper

I have the following system of differential equations, for the functions ##A(r)## and ##B(r)##: ##A'-\frac{m}{r}A=(\epsilon+1)B## and ##-B' -\frac{m+1}{r}B=(\epsilon-1)A## ##m## and ##\epsilon## are constants, with ##\epsilon<1##. The functions ##A## and ##B## are the two components of a...
15. ### Why chiral fermions don't exist in odd dimensions?

In four dimensions, left and right chiral fermion can be written as \psi_L= \begin{pmatrix} \psi_+\\ 0 \end{pmatrix},\qquad \psi_R= \begin{pmatrix} 0\\ \psi_- \end{pmatrix}, respectively, where \psi_+ and \psi_- are some two components spinors(Weyl spinors?). In this representation, the...
16. ### How Do Spinors Fit in With Differential Geometry

When I studied General Relativity using Misner, Thorne and Wheeler's "Gravitation", it was eye-opening to me to learn the geometric meanings of vectors, tensors, etc. The way such objects were taught in introductory physics classes were heavily dependent on coordinates: "A vector is a collection...
17. ### Substitution in the following supersymmetry transformation

I was reading in this book: Supergravity for Daniel Freedman and was checking the part that has to do with Extremal Reissner Nordstrom Black Hole. He was using killing spinors (that I am very new to). I was understanding the theory until he stated with the calculations: He said that the...
18. ### Spinors: Relativistic vs Non-Relativistic?

Consider the Spinor object for an electron. Are the non-relativistic and relativistic (Dirac equation) Spinor objects, from a mathematical point-of-view, identical? Thanks in advance.