One-particle distribution function (source code)

= One-particle distribution function
{title2=$f(x,p)$}

A scalar function on the future mass shell describing the expected particle count in a <phase-space distribution> cell. In a local <orthonormal tetrad>, the number crossing a spacelike surface element is $f\,p^\mu d\Sigma_\mu\,d^3p/E$. On a constant-time slice it becomes $f\,d^3x\,d^3p$. Including degeneracy and phase-space normalization in $f$ gives the <stress-energy tensor> $T^{\mu\nu}=\int(d^3p/E)fp^\mu p^\nu$. Other conventions may put the degeneracy or $(2\pi)^{-3}$ explicitly in the measure.