(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the anti-symmetric 4-tensor is a pseudotensor.

2. Relevant equations

[tex]\begin{eqnarray}

x'^0 &=& \gamma x^0 - \beta \gamma x^1 \\

x'^1 &=& \gamma x^1 - \beta \gamma x^0 \\

x'^2 &=& x^2 \\

x'^3 &=& x^3

\end{eqnarray}

[/tex]

3. The attempt at a solution

Under LT

[tex]

e'^{ijkl}=\frac{\partial x'^i}{\partial x^q} \frac{\partial x'^j}{\partial x^r} \frac{\partial x'^k}{\partial x^s} \frac{\partial x'^l}{\partial x^t} e^{qrst}[/tex]

I got that

[tex]\begin{eqnarray}

e'^{0123}&=&1 \\

e'^{1023}&=& -1 \\

e'^{0132}&=& -1 \\

e'^{1032}&=& 1

\end{eqnarray}

[/tex]

After doing these first few terms, I'm seeing through induction that [itex]e'^{ijkl}=e^{qrst}[/itex]. Which is what we want for a tensor, right? A pseudotensor should depend on the determinate of [itex]e'^{ijkl}[/itex]. What am I missing??

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# Levi Civita 4 tensor as pseudotensor

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