# Questions tagged [spinors]

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518 questions
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### Anti-commutative coordinates or Grassmann coordinates

In Supersymmetry, we have spinor generators. We have usual spacetime coordinates like $(x^\mu:t,x,y,z)$ and additional grassmann coordinates like $\theta^{\alpha},\bar{\theta}^\dot{\alpha}$.We know ...
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### Formal definition of gauge field and spinors in QFT

I am trying to pin down what spaces a spinor and gluon gauge field exactly occupy. I know that the spinor is a quantity $\psi_{i\alpha f}(\vec x, t)$ where $i$ is a color index in the fundamental ...
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### How this spinor identity is shown?

In one QFT problem it is asked to prove the following identity: $$\overline{u}_\sigma(p)\gamma^\mu u_{\sigma'}(p)=2\delta_{\sigma\sigma'}p^\mu.$$ Considering $u_\sigma$ the basis solutions to the ...
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### Coupling fermions with gravity

Einstein's gravity does not incorporate the "spinor" nature of fermions. The tetrad formulation or Cartan's theory is suggested as the way to go around this problem - by allowing the spin connection ...
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### Physical intuition of spin connection and spinor bundles?

I've been trying to learn about how to express the Dirac equation in curved spacetime, and in looking through various resources, I've found that the concepts of the spinor bundle and spin connection ...
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### Weinberg soft factor in spinor helicity

The leading order Weinberg soft factor is found to be $$\displaystyle\sum_{a=1}^{n}\frac{\epsilon^{\mu\nu}p_{\mu}p_{\nu}}{q.k_a},$$ where $a$ labels the external particles and $p$ denotes the ...
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### Six dimensional Weyl spinors and dimensional reduction

I am trying to understand spinors in 5+1 dimensions but I have troubles when going through dimensional reduction to 4+1 dimensions. The dimension of six dimensional Weyl representation is 4 and the ...
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### What, in natural language terms, does “spinor representation” mean (for students)?

Please look away if you’re an expert in Representation Theory… unless you’re happy to offer a helping hand to some tyros. To those of us – especially physical chemists and experimental physicists (...
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### What is the difference between a Pauli spinor, a Weyl spinor, and a Cartan spinor?

I know that a spinor is a complex two components "vector", which is acted on by the $SU(2)$ group under a rotation. In the physics litterature, I often read "Weyl spinors", "Pauli spinors", "Cartan ...
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### Why do we say that in non-relativistic limit we need only two component spinor?

Why do we say that in non-relativistic limit we need only two component spinor? (As in Schrödinger equation, we do not even talk of spinors,... they are one component object) I have read this ...
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### Spin Connection derivation in dirac equation

I'm learning about the spin connection, more specifically how it is derived in the dirac equation through this notes: http://web.phys.ntnu.no/~mika/CPP/ch15.pdf In the third page of the document it ...
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### Variation of the Spin Connection

I am trying to get an explicit expression for the variation $\delta \omega_{\mu}^{\ ab} / \delta e_\mu^a$, but when doing the actual variation I end up with a series of 16 terms that I cannot simplify ...
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### polarized trace

Lets say I want to calculate the following Trace $\mathrm{Tr}[u^{s_1}(p)~\bar{u}^{s_2}(p)~\gamma^{\mu}\not p~ \not q~ \not p~ \gamma^\nu]$ Now if I consider unpolaized case then $s_1=s_2=s$ and I ...
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### Does the form of fermion multiplet change with gauge symmetry representation?

The covariant derivative for a fermion with a symmetry group $SU(N)$ is given by $$D_\nu \psi = \partial_\nu \psi -i g A^A_\nu t_A \, \psi, \tag{1}$$ where $A^A_\nu$ is a gauge field, $g$ is a ...
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### Geometric meaning of killing spinor?

I know about killing vectors- They forms the basis for the isometries of a metric space. I am not clear about the definition of killing spinors, in the sense the one there is for killing vectors, ...
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### How to transform Dirac fermion coupled with $SU(2)/Z_2$ gauge field to the real fermion coupled with $SO(3)$?

For instance, I am considering a free (3+1)-D Dirac fermion coupled with $SU(2)$ (fundamental representation) gauge field. Then I do a "gauging" the center $Z_2$ to the associated principal bundle by ...
In Peskin-Schroeder Chapter 3.3: Free Particle Solutions of the Dirac Equation the form of the general Dirac Spinor $u(p)$ along 3-direction is derived from $u(p_0)$ in the system of rest by applying ...