# Questions tagged [dirac-matrices]

Dirac matrices, or gamma matrices, are a set of matrices with specific anticommutation relations that generate a matrix representation of the Clifford algebra which acts on spinors, fundamental to the Dirac equation describing spin-1/2 charged particles.

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### Derivation of covariant derivative of Spinor

I am following this derivation for the covariant derivative of spinors. I have some questions about this derivation: On page 3 they use the fact, that \begin{align*} V^a(x) = \bar{\Psi}(x)\gamma^a\...
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### What is the correct way of looking at the Dirac field?

All quantum fields are operators in QFT. However, the Dirac field operator $\hat{\psi}$ has the following difference with the scalar field operator $\hat{\phi}$: For the $\hat{\psi}$, it makes sense ...
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### Is there a fast way to simplify gamma matrix tensors?

I’m doing QFT homework, and our professor said Fermions require a lot of algebra. And I’m finding he’s right. I want to either get a mastery of these operations or find useful shortcuts. Since it’s ...
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### Srednicki eq. (1.27): $\left\{\alpha^{j}, \alpha^{k}\right\}_{a b}=2 \delta^{j k} \delta_{a b}$

Srednicki, QFT, p. 8 writes $$\left\{\alpha^{j}, \alpha^{k}\right\}_{a b}=2 \delta^{j k} \delta_{a b}\tag{1.27}.$$ What does exactly $ab$ here denote? Assume I have a matrix X [0 1] [2 3] and does a ...
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### Witten on the hermitian of the Dirac operator

I happened to read Witten SU(2) anomaly paper (1982), and come back to digest again what I said the hermitian of the Dirac operator. According to Prahar https://physics.stackexchange.com/a/701287/...
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### Is the Dirac operator $i \not D$ or $\gamma^0 i \not D$ and nonabelian gauge field $A_\mu = A_\mu^\alpha T^\alpha$ hermitian?

In quantum mechanics, it is common to write the momentum operator $$P = i \partial_x.$$ It turns out that $p$ is hermitian although $i^\dagger = -i$ we also have $\partial_x ^ \dagger=-\partial_x$. It ...
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### What is the deep connection between the two ways to get Pauli matrices?

The first way is the one in which we start with the commutator relations $[J_x, J_y]=ihJ_z$, etc. We consider the simultanelus eigenbasis of $J^2$ and $J_z$ : $|j,m\rangle$. We then obtain their ...
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### How to calculate the trace of six gamma matrices multiplied to $\gamma_5$?

I read from Weinberg that, the gamma matrices have the following property: \begin{equation} \text{Tr}\{\gamma_5 \gamma_\mu \gamma_\nu \gamma_\rho \gamma_\sigma\}=4i\epsilon_{\mu \nu \rho \sigma} \end{...
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