Affine momentum normalization of a geodesic

For physical four-momentum $P^{\mu }=md{x}^{\mu }/d\tau$, the covariant-component equation is $d{P}_{\mu }/d\tau =({\partial }_{\mu }{g}_{\nu \sigma })P^{\nu }{P}^{\sigma }/(2m)$. The equation without $1/m$ instead uses a tangent parametrization, or the affine parameter $\lambda =\tau /m$ when the tangent is the physical momentum.