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- 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?

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?