- #1

user1139

- 72

- 8

- Homework Statement:
- Write out $$F_{\alpha\beta}F^{\alpha\gamma}$$ in a simplified sum where $$F$$ is the stress tensor and Einstein summation convention is implied.

- Relevant Equations:
- $$F_{\mu\nu}$$ is the usual stress tensor

I managed to write

$$F_{\alpha\beta}F^{\alpha\gamma}=F_{0\beta}F^{0\gamma}+F_{i\beta}F^{i\gamma}$$

where $$i=1,2,3$$ and $$\gamma=0,1,2,3=\beta$$.

How do I proceed?

$$F_{\alpha\beta}F^{\alpha\gamma}=F_{0\beta}F^{0\gamma}+F_{i\beta}F^{i\gamma}$$

where $$i=1,2,3$$ and $$\gamma=0,1,2,3=\beta$$.

How do I proceed?