= Weyl Hamiltonian
{c}
{title2=$H=v\boldsymbol\sigma\cdot\mathbf p$}
The isotropic <Weyl Hamiltonian> acts on a two-component <spinor> as $H=v\boldsymbol\sigma\cdot\mathbf p$. For a <plane wave> of momentum $\hbar\mathbf k$, its two <energy eigenvalues> are $E_\pm=\pm\hbar|v||\mathbf k|$. For $v>0$ the corresponding <Bloch vectors> point along and opposite $\mathbf k$, respectively. If the <Pauli matrices> describe physical <spin one-half>, the mean spin is $\pm(\hbar/2)\widehat{\mathbf k}$; in an effective two-band model the same algebra can describe an internal pseudospin instead. The bands meet linearly at the origin. https://www.damtp.cam.ac.uk/user/tong/gaugetheory/4lattice.pdf[David Tong, Gauge Theory, §4.3.2, continuum Hamiltonian near equation (4.26)]{ref}
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