I set eyes on the next formulas:(adsbygoogle = window.adsbygoogle || []).push({});

\begin{align}

E_{\alpha \beta \gamma \delta} E_{\rho \sigma \mu \nu} &\equiv g_{\alpha \zeta} g_{\beta \eta} g_{\gamma \theta} g_{\delta \iota} \delta^{\zeta \eta \theta \iota}_{\rho \sigma \mu \nu} \\

E^{\alpha \beta \gamma \delta} E^{\rho \sigma \mu \nu} &\equiv g^{\alpha \zeta} g^{\beta \eta} g^{\gamma \theta} g^{\delta \iota} \delta^{\rho \sigma \mu \nu}_{\zeta \eta \theta \iota} \\

E^{\alpha \beta \gamma \delta} E_{\rho \beta \gamma \delta} &\equiv -6 \delta^{\alpha}_{\rho} \\

E^{\alpha \beta \gamma \delta} E_{\rho \sigma \gamma \delta} &\equiv -2 \delta^{\alpha \beta}_{\rho \sigma} \\

E^{\alpha \beta \gamma \delta} E_{\rho \sigma \theta \delta} &\equiv -\delta^{\alpha \beta \gamma}_{\rho \sigma \theta} \,.

\end{align}

in https://en.wikipedia.org/wiki/Levi-Civita_symbol#Levi-Civita_tensors I want to know for what signature (+---) or (-+++) it is given. Is there simple way to check signature?

In my opinion there are need plus rather than minus at least in last three formulas:

\begin{align}

E^{\alpha \beta \gamma \delta} E_{\rho \beta \gamma \delta} &\equiv 6 \delta^{\alpha}_{\rho} \\

E^{\alpha \beta \gamma \delta} E_{\rho \sigma \gamma \delta} &\equiv 2 \delta^{\alpha \beta}_{\rho \sigma} \\

E^{\alpha \beta \gamma \delta} E_{\rho \sigma \theta \delta} &\equiv \delta^{\alpha \beta \gamma}_{\rho \sigma \theta} \,.

\end{align}

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Levi-Civita symbol in Minkowski Space

Tags:

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**