- #1

merhalag

- 2

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## Homework Statement

Hi every one, I am really confused on how to calculate the inverse of this Levi Civita symbole's element [itex]\epsilon^{tabc}[/itex], I tried to used this equation [itex]\epsilon^{\mu\nu\rho\sigma}\epsilon_{\mu\nu\alpha\beta}=\delta^{\rho}_{\alpha}\delta^{\sigma}_{\beta}-\delta^{\rho}_{\beta}\delta^{\sigma}_{\alpha}[/itex]

## Homework Equations

In fact I am searching [itex]\left(\epsilon^{tabc}\right)^{-1}[/itex] where the indices should be lower.

## The Attempt at a Solution

Based on the equation above, is it correct if I write: [itex]\epsilon_{taef}\epsilon^{tabc}=\delta^{b}_{e}\delta^{c}_{f}-\delta^{b}_{f}\delta^{c}_{e}[/itex]

I recall that [itex]\mu\nu\rho\sigma...[/itex] are the diffeomorfism indices on curved space-time, "t" is the temporal indice and where "a,b,c..." are the spatial ones.

I apologize for my bad english once again. I have tried to do my best to make the problem statement as clear as possible.