# Dirac matrices in 2 dimensions and $\gamma_5$

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.

• 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? – ACuriousMind Jun 1 at 11:34
• chirality only exists in even dimensions. – AccidentalFourierTransform Jun 1 at 12:48
• Are you cool with the general picture? – Cosmas Zachos Jun 1 at 13:24
• @AccidentalFourierTransform How is that? Does it exist in (1+1)D right? – Andreu Heisenberg Jun 1 at 14:24
• @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? – Andreu Heisenberg Jun 1 at 14:27