Four momentum vector from energy-momentum-tensor

1. Jul 28, 2009

torus

Hi,
for a real scalar field one has the energy momentum tensor from Noethers theorem
$$T^{\mu\nu} = \frac{\partial \mathcal{L}}{\partial \partial_\mu \phi} \partial^\nu \phi - \eta^{\mu\nu} \mathcal{L}$$
and the conserved quantities
$$P^\nu = \int d^3 x \ T^{0\nu}$$

Now, how can one show that P is really a 4-vector, since the definition looks not that covariant and I could not think of anything.