 #1
Frostman
 114
 17
 Homework Statement:
 Construct the energymomentum tensor for a relativistic system of noninteracting particles and show explicitly that it is conserved.
 Relevant Equations:

##T^{\alpha\beta}=\frac{\partial L}{\partial \varphi/_\alpha}\varphi/^\betag^{\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 noninteracting particles.
For a free relativistic particle I know that lagrangian is:
$$L=\frac{m_0}{\gamma}$$
But for a system of noninteracting particles I can use this one?
$$L=\sum_i\frac{m_{0i}}{\gamma}$$
But when I step to energymomentum tensor I don't have any covariant formalism in this lagrangian. Somebody can help me?
For a free relativistic particle I know that lagrangian is:
$$L=\frac{m_0}{\gamma}$$
But for a system of noninteracting particles I can use this one?
$$L=\sum_i\frac{m_{0i}}{\gamma}$$
But when I step to energymomentum tensor I don't have any covariant formalism in this lagrangian. Somebody can help me?