All Questions
Tagged with group-theory spinors
118
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What is the connection between Lorentz transforms on spinors and vectors?
When deriving the (1/2,0) and (0,1/2) representations of the Lorentz group one usually starts by describing how points in Minkowski space transform while preserving the speed of light (or the metric).
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2
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1
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Helicity operator in spinor-helicity variables
How do I prove that the helicity operator is
$$
H = \frac{1}{2} (\tilde{\lambda}_\dot{\alpha} \frac{\partial}{\partial \tilde{\lambda}_\dot{\alpha}} - \lambda_\alpha \frac{\partial}{\partial \lambda_\...
- 191
8
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Can we make a Bloch sphere for Weyl spinors?
If spinors are the "square root" of 3-vectors [$\mathrm{SU}(2)$ double cover of $\mathrm{SO}(3)$], Weyl spinors can be thought of as the "square root" of 4-vectors [$\mathrm{SL}(2,\...
- 5,568
19
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4
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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 ...
- 512
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Weyl spinors under the Lorentz transformation
I am reading An Modern Introduction to Quantum Field Theory by Maggiore. On page 28, it says
Using the property of the Pauli matrices $\sigma^2 \sigma^i \sigma^2 = -\sigma^{i*}$ and the explicit form ...
- 41
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Represent the Pauli 4-vector $\sigma^\mu$ as hermitian matrix of matrices due to the $SL(2,C)$ universal double cover of $SO^+(3,1)$
It's known that it's possible to map a 4-vector $x^\mu=(t,x,y,z)$, here i use $c=1$, into a 2x2 hermitian matrix as linear combination of Pauli matrices, thus the mapping $x^\mu \leftrightarrow X$. ...
- 310
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What justifies the statement that a Dirac spinor can be written as two Weyl spinors?
I've cross listed this post on math SE in case it is more appropiate there. That post can be found here: https://math.stackexchange.com/q/4833722/.
I am approaching this from a Clifford algebra point ...
- 3,350
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Building 4-vectors out of Weyl spinors: Combining 2 independent Weyl spinors and a sigma matrix to get a 4-vector
i'm struggling with this problem
In Exercise 2.3 of A Modern Introduction to Quantum Field Theory of Michele Maggiore I am asked to show that, if $\xi_R$ and $\psi_R$ are right-handed spinors, then
$$...
- 310
4
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1
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266
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Understanding spinors, double cover and professor's expanation
I'm following an introductory course in QFT, and we are facing the spin group part. I think that most of the details are left apart because it would take too much time to be developd, and my profesor ...
- 361
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Understanding Wikipedia's definition of a spinor
I originally asked this question on math SE but I'm asking it again here due to the lack of responses. I should note that I come from a mathematical background and not a physics one so I am not ...
- 3,350
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Are representations of (bosonic) Lie groups over Grassmann variables well understood?
When one studies representations of (bosonic) Lie groups in physics, whether dealing with spacetime symmetries or gauge symmetries, it is often left implicit whether the representations are over real ...
- 1,117
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Question about spinor inner products
Let a 2D spinor be given by
$$\chi_2(p)=\pmatrix{\xi^1\\\xi^2}+i\pmatrix{\xi^3\\\xi^4}$$
with the $\xi^i$'s being real for $i=\{1,2,3,4\}$.
Assume, now, that I want to represent this spinor by a real-...
- 3,992
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Seeking Spinor Operation Analogous to $M^T \eta M = g$ for GL$^+(4,\mathbb{R})$/Spin$^c$(3,1)
I'm exploring the spinorial representation of the Spin$^c$(3,1) group, especially in the context of metric preservation in general relativity and quantum field theory.
For the group GL$^+(4,\mathbb{R}$...
- 1,548
1
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1
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196
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Why the Double Covering?
It is known mathematically that given a bilinear form $Q$ with signature $(p,q)$ then the group $Spin(p,q)$ is the double cover of the group $SO(p,q)$ associated to $Q$, and that $Pin(p,q)$ is the ...
- 1,611
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Why the symmetry is not $Pin(1,3)$ or $Pin(3,1)$ in condensed matter physics?
In usual electron systems (or condensed matter physics), it is well known that $T^2=-1$ and $M^2=-1$, where $T$ and $M$ are time reversal and reflection along some axis. But in general, the symmetry ...
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