= Kinetic stress-energy tensor
{title2=$T^{\mu\nu}=\int\frac{d^3p}{E}f p^\mu p^\nu$}
The invariant future mass-shell measure is $d^3p/E$, up to fixed normalization factors absorbed in $f$. Its relation to the <Lorentz-invariant phase-space measure> follows by integrating $2\theta(p^0)\delta(p_\mu p^\mu+m^2)\,d^4p$ over $p^0$ in a local <orthonormal tetrad>. A particle carries <four-momentum> $p^\mu$ and crosses a local spatial surface with velocity $p^i/p^0$. Integrating the associated <momentum flux> gives the displayed <stress-energy tensor>. For <photons>, $p^{\hat a}=E(1,\mathbf e)$ and $|\mathbf e|=1$.
Back to article page