# Questions tagged [dirac-matrices]

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### Do Dirac Gamma Matrices act like Tensors?

Do Dirac Gamma Matrices act like Tensors? Is it true that $$\gamma_\mu = \eta_{\mu\nu}\gamma^\nu~?$$ Also what about $\sigma_{\mu\nu}$, where $\sigma_{\mu\nu}$ is defined to be: \begin{align*} \...
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### Why in the relativistic quantum mechanics $\gamma_4$ name is not used instead of $\gamma_5$?

I have seen in the in the Dirac equation $$\gamma_0,\gamma_1,\gamma_2,\gamma_3.$$ Then I have seen the definition of a new matrix $$\gamma_5=i\gamma_0\gamma_1\gamma_2\gamma_3.$$ Now my question is why ...
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### What is unitarily similar matrices?

In one of tasks I met the concept of unitarily similar matrices: in particular, I need to prove that sets $\gamma_{\mu}, -\gamma_{\mu}$ (Dirac gamma matrices) are unitarily similar. I don't know what ...
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The trace of matrix is always sum of its eigen values , which can be seen if $\hat{U}$ transforms the matrix $\alpha_i$ into it's diagonal form . $$\begin{pmatrix} A_1 & 0 & \cdots & 0 \... 0answers 249 views ### Are Lifshitz and Berestetskii right in this case? In the Quantum electrodynamics book (look at the problem) its authors Lifshitz and Berestetskei claim that operator of charge conjugation \hat {C} = -\alpha_{2} in Majorana basis transforms as \hat ... 2answers 2k views ### Why the lowest order of matrices in Dirac equation are 4x4 matrices? [duplicate] Why the lowest order of matrices in Dirac equation (Relativistic Quantums) are 4x4 matrices (and can not be 2x2 matrices)? How to prove it? 1answer 1k views ### Closed formula for product of gamma matrices I was asking myself if there is a closed formula for the following product of gamma matrices:$$\gamma_\mu\gamma_\nu \gamma_5.$$I would like to express this matrix in terms of the basis$${\...
The spinor inner product in particle physics is given by $\overline{\psi} \psi = \psi^{\dagger} \gamma_0 \psi$, where I take the convention that the zeroth gamma matrix is hermitian while the rest ...