- #1
torus
- 20
- 0
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.
Thanks for your response,
torus
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.
Thanks for your response,
torus
