# Levi-Civita 4D

1. Oct 2, 2013

### Petraa

1. The problem statement, all variables and given/known data

I was following this book "problem book in quantum field theory by voja radovanovic" and I got stuck in the following problem

Prove $\epsilon_{\alpha\beta\gamma\delta}A_{\,\nu}^{\alpha}A_{\,\mu}^{\beta}A_{\,\lambda}^{\gamma}A_{\,\sigma}^{\delta}=\epsilon_{\mu\nu\lambda\sigma}\det\left(A\right)$

2. Relevant equations

A is a matrix and in the left-hand side we have the components of this matrix

3. The attempt at a solution

I've tried to write an explicit form for the determinant using

$\det\left(A\right)=\sum_{i_{1}...i_{n}}\epsilon_{i_{1}}...\epsilon_{i_{n}}A_{1,i_{1}}...A_{n,i_{n}}$

but i didn't find anything useful. Any help or tip would be appreciated

Thank you