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The gamma matrices obeying the Clifford algebra can be represented by Pauli matrices in (1+1) and in (1+2) dimensions. But is it possible to define a $\gamma_5$ in these dimensions? In the sense of an analogous way of how $\gamma_5=i \gamma_0\gamma_1\gamma_2\gamma_3$ is defined in 4D.

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    $\begingroup$ What do you mean by "a $\gamma_5$"? You can just write down the product of all gamma matrices regardless of dimension. What exactly do you want to know? $\endgroup$ – ACuriousMind Jun 1 at 11:34
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    $\begingroup$ chirality only exists in even dimensions. $\endgroup$ – AccidentalFourierTransform Jun 1 at 12:48
  • $\begingroup$ Are you cool with the general picture? $\endgroup$ – Cosmas Zachos Jun 1 at 13:24
  • $\begingroup$ @AccidentalFourierTransform How is that? Does it exist in (1+1)D right? $\endgroup$ – Andreu Heisenberg Jun 1 at 14:24
  • $\begingroup$ @CosmasZachos yeah, that kind of works for me. Following the previous comment, would, in (1+1)D, $\gamma_0$ and $\gamma_1$ constitute the Dirac matrices and $\gamma_5 = \gamma_0 \gamma_1$ the chiral one? But in (1+2)D, the Dirac matrices are $\gamma_0$, $\gamma_1$ and $\gamma_5 = \gamma_0 \gamma_1$, but no chirality matrix is present? $\endgroup$ – Andreu Heisenberg Jun 1 at 14:27

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