# Tagged Questions

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### What is the point of path integral for boson and fermion?

I am a beginner to study QFT and confused about path integral for boson or fermion. I have read about the path integral for single particle, and finished some problems. But I cannot understand the ...
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### Spinor representation of $SO(d+1,1)$

I have been looking over the internet for a resource that tells me the number of dimensions of a spin $s-1$ spinor representation of $SO(d+1,1)$, but unfortunately have yet to be able to find it. In ...
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### Direct sum of the spinors and EM field tensor

EM field tensor refer to the direct sum of $(1, 0), (0, 1)$ spinor representation of the Lorentz group. How to show it? Each of these spinor representations corresponds to the symmetrical spinor ...
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### Can we build spinorial eigenstates of Time reversal symmetry?

In the SM, and general theories with spinors, we can build the Parity left/right eigenspinors. Indeed, there are also ELKO fields, eigenstates of Charge operator (non-standard Wigner classes). Can we ...
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### Spin half particle Magnetic field oriented along y-axis

I've been looking over past papers for an upcoming QM exam and have had a few issues wrapping my head around this question. I can follow the common example as seen in Griffiths where the field is ...
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### Spin structure for SOC spin-1/2 system

It is well known that we have a $\mathbb{Z}_2$ extension of any symmetry group acting on a half-integer spin fermion system. Now if we also have spin-orbit coupling, what is the spin structure that we ...
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### Probability density for spinors

I am approaching Relativistic Quantum Mechanics seriously for the first time, going through Bjorken & Drell and doing all the excercises, but I am facing some problems with 3.1. Derive (3.11) ...
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### Spinor helicity formalism - original reference?

The spinor helicity formalism is a modern technique widely used in scattering amplitude calculations nowadays. However, it is hard to find a reference for who first came up with the formalism. Maybe ...
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### Confusion over trying to understand spinor components

I've been reading about the quantisation of the Dirac field $\psi(x)$ and it is stated that the general solution to the Dirac equation $(i\gamma^{\mu}\partial_{\mu}-m)\psi(x)=0$ is given by the ...
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### Solving Weyl Equations

In my second taking of QFT we just finished the Dirac equation. As an exercise I tried applying what I have (re-) learned to the Weyl equations. I'd like someone to check if my work is correct. For ...
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### Cyclicity of trace with fermionic arguments

I think this is a non-question, but it has me considerably worried. Consider the piece of a Lagrangian density given by, \mathcal{L} = \epsilon_{ij}\mbox{Tr}\left(\chi^{i,\alpha}\left[\chi^{j}_\...
I'm reading about twistors from the book of Huggett and Tod: $\textit{ An introduction to twistor theory}$. I'm trying to understand everything and reproduce every equation that comes here. So, ...
### A Lie derivative $\mathcal{L}_{\alpha^A}$ with respect to a spinor $\alpha^A$?
Suppose we work with Minkowski flat space $M$ (just to make things easy). If $\textbf X$ is a Killing vector field it is possible to define the Lie derivative of an spinor $\alpha^A$ with respect to \$\...