= Boost charge of a one-dimensional scalar field
{title2=$J^{01}=tP-\int x\mathcal E\,dx$}
For a free massless real <scalar field> with <wave speed> set to one and metric $(+,-)$, define $\mathcal E=(\phi_t^2+\phi_x^2)/2$ and $p=-\phi_t\phi_x$. Its symmetric <stress-energy tensor> is $T^{\mu\nu}=\left(\begin{smallmatrix}\mathcal E&p\\p&\mathcal E\end{smallmatrix}\right)$. The <Lorentz current> has density $t p-x\mathcal E$ and flux $t\mathcal E-xp$. Its conserved charge is the displayed expression when boundary flux vanishes. In one spatial dimension it generates boosts, not spatial rotations; there is no independent purely spatial angular-momentum component. Its conservation says that the center of energy moves uniformly. This is a symmetry of the wave-field model and need not survive boundaries or additional material effects.
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