Is the Levi-Civita symbol a tensor?
R. A. Sharipov afirm (In "Quick Introduction to Tensor Analysis", page 30) that "…the Levi-Civita symbol is NOT a tensor…"
$\epsilon_{jkq}=\epsilon^{jkq}=\left\{\begin{array}{rl} 0, & \mbox{if among $j$, $k$, $q$ there are at least two equal numbers} \\ 1, & \mbox{if $(j,k,q)$ is even permutation of numbers $(1,2,3)$} \\ -1, & \mbox{if $(j,k,q)$ is odd permutation of numbers} \end{array}\right.$
What does that phrase mean?
Thanks!
Best Answer
I had this same question and I found this: http://www.physics.ucc.ie/apeer/PY4112/Tensors.pdf Page 11, it explains that the Levi-Civita Symbol is a Tensor Density and transforms it using to a tensor the same way that Sharipov did it (and explains the steps).