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 - The Fusion of Science and Community**

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

Loading...

Similar Threads - Levi Civita symbol | Date |
---|---|

A Algebraic Proofs of Levi-Civita Symbol Identities | Jul 3, 2017 |

A Contraction between Levi-Civita symbol and Riemann tensor | Dec 22, 2016 |

Levi-Civita Connection and Derivative of The Ricci Scalar | Aug 31, 2015 |

Levi-Civita symbol | Jan 15, 2012 |

Upper- and lower-index Levi-Civita tensor/symbol | Oct 31, 2010 |

**Physics Forums - The Fusion of Science and Community**