# Questions tagged [spinors]

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### How to derive this form of helicity spinor (massless/high energy limit)

Srednicki 50.7 says that in the massless limit, we can express $$u_-(\textbf{p})\bar{u}_-(\textbf{p}) = \begin{pmatrix} 0&-p_{a\dot{a}}\\0&0\end{pmatrix}$$ This comes from a previously ...
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### Yukawa Theory with Spinor Helicity Formalism

I am trying to learn spinor helicity formalism, and I am attempting to calculate the all-minus amplitude of 4-fermion scattering at tree level in Yukawa theory, but I have no way to check if my ...
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### Question about meaning of "bar"-ing in the context of Dirac fields

Following chapter 38 of Srednicki, "bar"-ing means (based on eq. 38.15) $$\bar{A} = \beta A^\dagger\beta$$ One can show for instance that $$\bar{\gamma^\mu} = \gamma^\mu$$ My question is, ...
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### How to rotate an electron mathematically?

Im a mathematics student who just learned about the fact that if you rotate an electron by $2 \pi$ its spin state changes but if you turn it by $4 \pi$ it stays the same. I understand all the ...
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### Prove that spinors satisfying the Killing equation lives on a sphere

Considering that the covariant derivative $D_{\mu}$ acting on spinors be given by $$D_{\mu} \eta = \pm \frac{i}{2} \gamma_{\mu} \eta$$ It is claimed that theses spinors lives on a constant curvature ...
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I am trying to understand the different combinations of quarks in a hadron. I have seen that the positive pion is written as $\pi^{+}=u\bar{d}$, but I have not seen it written in the opposite order. ...
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### Non-relativistic limit of time-dependent Dirac equation

Can someone point me to the derivation of the non-relativistic limit of the time-dependent Dirac equation? I'm presuming that the limit is nothing but the time-dependent Schrodinger equation. I ...
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### How to define spinors in general relativity?

In Schwartz's QFT and the Standard Model, a vector is defined an object that transforms like a vector. For instance, $V$ is a 4-vector if its components transform like this under Lorentz boost, \begin{...
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### Can spinors be explained or understood without group or representation theory?

Vectors, either as abstract mathematical elements of a vector space (in this case the definition of the vector is divorced from any notion of transformation), or as elements of tangent spaces on ...
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### Why the massive spin-1 photon gets more degrees of freedom than massless case; while the massive spin-1/2 electron stays the same as massless case?

Spin 1 field without mass term like photon has 2 real degrees of freedom. The polarization with two states. I think I can denote it as quantum state $|s,s_z> = |1,1>$ and $|1,-1>$. Spin 1 ...
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### Physical significance of left- and right-handed spinors

We know that the $(1/2,0)$ and $(0,1/2)$ representations of Lorentz group represent the left- and right-handed spinors respectively. What’s the reason behind this nomenclature? What they represent ...
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