# Showing the invariance of Levi-Civita symbol in 4 dimensions

1. May 1, 2017

### Phys pilot

1. The problem statement, all variables and given/known data
i am showing the invariance of the Levi-Civita symbol in 4 dimensions
3. The attempt at a solution
$$\varepsilon_{ijkl}'=R_{im}R_{jn}R_{kp}R_{lt}\varepsilon_{mnpt}$$
$$\varepsilon_{ijkl}\varepsilon_{ijkl}'=\varepsilon_{ijkl}\varepsilon_{mnpt}R_{im}R_{jn}R_{kp}R_{lt}=4!\det{R}=4!$$

$$\varepsilon_{ijkl}\varepsilon_{ijkl}'=4!$$

so then
$$\varepsilon_{ijkl}=\varepsilon_{ijkl}'$$

2. May 6, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.