All Questions
8
questions
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votes
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answers
54
views
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
0
votes
0
answers
47
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$S$-operator for proper Lorentz transformation
By applying infinitesimal Lorentz transformatios successively (with rotation angle $\omega$ around the $\bf n$ axis) one would get
$$\Psi'(x') = \hat{S}\Psi(x) = e^{-(i/4)\omega\hat{\sigma}_{\mu\nu}(\...
- 45
1
vote
0
answers
81
views
Derivation of the transformation law for spinors
I'm reading the book Quantum Field Theory: An Integrated Approach by Eduardo Fradkin, and I got stuck where the transformation law for spinors
$$
\psi'(x') = S(\Lambda) \psi(x)
$$
is derived.
In ...
- 601
0
votes
1
answer
146
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Quantum Field Theory Unitary Transformations
I am currently reading through Itzyskon and Zuber for my quantum field theory class, and I came across this regarding the unitary transformations of the Dirac bispinors in chapter 2. They show that ...
- 329
1
vote
1
answer
1k
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Lorentz boost of Dirac spinor
Let $\psi_\vec{0}^+$ be a Dirac wavefunction describing a motionless particle,
$$\psi_\vec{0}^+(x) = \sqrt{2m} \begin{pmatrix}
\chi \\
0
\end{pmatrix} e^{ip \cdot x}$$
where $p = (m, \vec{0})$. ...
- 653
1
vote
2
answers
1k
views
Lorentz transformation of a Weyl Spinor?
A left handed Weyl Spinor belongs to the $(\frac{1}{2},0)$ representation of the Lorentz group. So given the Spinor, the unitary representation of the Lorentz transformation should look like $\exp{iA\...
- 3,514
1
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0
answers
79
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Spinor Lorentz Transformation
Why should the transformation between the solutions of the Dirac equation for different inertial observers be linear?
- 39
29
votes
3
answers
12k
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Lorentz transformation of Gamma matrices $\gamma^{\mu}$
From my understanding, gamma matrices transforms under Lorentz transformation $\Lambda$ as
\begin{equation}
\gamma^{\mu} \rightarrow S[\Lambda]\gamma^{\mu}S[\Lambda]^{-1} = \Lambda^{\mu}_{\nu}\gamma^{\...
- 595