# Energy-momentum tensor for a relativistic system of particles

Frostman
Homework Statement:
Construct the energy-momentum tensor for a relativistic system of non-interacting particles and show explicitly that it is conserved.
Relevant Equations:
##T^{\alpha\beta}=\frac{\partial L}{\partial \varphi/_\alpha}\varphi/^\beta-g^{\alpha\beta}L##
##T^{\alpha\beta}/_\alpha=0##
I think it is quite simple as an exercise, following the two relevant equations, but at the beginning I find myself stuck in going to identify the lagrangian for a relativistic system of non-interacting particles.
For a free relativistic particle I know that lagrangian is:
$$L=-\frac{m_0}{\gamma}$$
But for a system of non-interacting particles I can use this one?
$$L=\sum_i-\frac{m_{0i}}{\gamma}$$
But when I step to energy-momentum tensor I don't have any covariant formalism in this lagrangian. Somebody can help me?