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Levi-Civita 4D

  1. Oct 2, 2013 #1
    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 [itex]\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)
    [/itex]

    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

    [itex]
    \det\left(A\right)=\sum_{i_{1}...i_{n}}\epsilon_{i_{1}}...\epsilon_{i_{n}}A_{1,i_{1}}...A_{n,i_{n}}[/itex]

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

    Thank you
     
  2. jcsd
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