= Dirac field in two spacetime dimensions
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{title2=$\gamma^0=\sigma_1,\quad\gamma^1=-i\sigma_2,\quad\gamma^5=\sigma_3$}
For <Minkowski metric> $\operatorname{diag}(1,-1)$, the displayed <gamma matrices> satisfy the <Clifford algebra> and $\gamma^5=\gamma^0\gamma^1$ has <chirality> <eigenvalues> $+1,-1$. Ordering the <spinor> as $(\psi_R,\psi_L)^{\mathsf T}$ gives $i(\partial_t+\partial_x)\psi_R=m\psi_L$ and $i(\partial_t-\partial_x)\psi_L=m\psi_R$. A <plane wave> has the <Dirac Hamiltonian> $p\sigma_3+m\sigma_1$, whose square is $(p^2+m^2)1$, proving $E^2=p^2+m^2$.
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