# Is a symmetric Lagrangian leads to a symmetric Stress-Energy Momentum？

1. Jul 2, 2010

### centry57

Is a symmetric Lagrangian leads to a symmetric Stress-Energy Momentum ？

2. Jul 2, 2010

### blechman

A "symmetric energy momentum tensor" obeys $T_{\mu\nu}=T_{\nu\mu}$.

A Lagrangian is a scalar, with no indices.

So what does one have to do with another?

3. Jul 2, 2010

### centry57

I was adoubt if a symmetric stress-energy tensor 's lagrangian is symmetry .

Since ${\cal L}= - \frac{1}{16\pi}F^{\mu\nu} F_{\mu\nu}$ is symmetry on \mu &\nu,the corresponding Stress-Energy Tensor $\Theta^{\mu}\,_{\nu} = - \frac{1}{4 \pi} F^{\mu \alpha} \partial_{\nu}A_{\alpha} + \frac{1}{16\pi} \delta^{\mu}_{\nu} F^{\alpha\beta}F_{\alpha\beta}$ is also symmetry.

Is this the special one ?

Last edited: Jul 2, 2010