 Transverse interference current of Weyl wave packets

For a coherent two-component field $\psi =e^{-i{V}_{0}t}(\eta (t-z),\rho (t+z){)}^T$, the physical current is $\mathbf{J}=(2\mathrm{Re}{\eta }^{\ast }\rho ,2\mathrm{Im}{\eta }^{\ast }\rho ,|\eta {|}^2-|\rho {|}^2)$. The density is $|\eta {|}^2+|\rho {|}^2$. Transverse components generally survive interference even though the field has no transverse coordinate dependence. They have zero transverse divergence; together with the longitudinal current they obey local conservation and $|\mathbf{J}{|}^2=({\psi }^{†}\psi {)}^2$.