# 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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### $CP$-transformation for fermionic bilinears

I am trying to derive the transformation of the fermionic bilinear $\bar{\psi}\psi$ under $CP$ transformation. I know that $P$ acts as: $$\psi(t, \vec{x}) \xrightarrow{P} \gamma^0 \psi(t, -\vec{x})$$ ...
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### Does $\alpha$ and $p$ commute where $\alpha$ is a Dirac matrix and $p$ is a momentum operator?

Can I write $\langle\psi\vert\alpha.p\vert\psi\rangle$ as $\langle\psi\vert p.\alpha\vert\psi\rangle$ ?
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### Time reversal operator and Dirac gamma matrices

How would you prove that $T^{-1}\gamma_\mu T=\gamma_\mu$? Being $T$ the time reversal operator defined as $T=\gamma_1\gamma_3 K$ with $K$ the complex conjugate operator and $\gamma$ the Dirac gamma ...
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### Is the solution of the Dirac equation supposed to be a $4\times 4$ matrix?

Rearranging the Dirac Equation, we find that $$\sum_\mu\gamma^\mu \partial_\mu \psi = -imc\frac{2\pi}{h} \psi.$$ It appears that the wavefunction times the constant is equal to the matrix result of ...
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