- #1

dRic2

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- Homework Statement:
- Show that the components of the totally antisymmetric symbol ##\epsilon^{\mu \nu \alpha \beta}## are invariant under transformation belonging to SO(3,1) group.

- Relevant Equations:
- .

Hi, I'm reading some introductory notes about SR and I'm completely stuck at this problem. I imagine I should consider a transformation ##L## such that

$$ \hat \epsilon^{\mu \nu \alpha \beta} = L^{\mu}_{\delta}L^{\nu}_{\gamma}L^{\alpha}_{\theta}L^{\beta}_{\psi} \hat \epsilon^{\delta \gamma \theta \psi}$$

and somehow play around with the LHS to show it is equal to ##\epsilon^{\mu \nu \alpha \beta}##. Am I right ? Problem is I'm completely out of ideas.

Thanks

Ric

$$ \hat \epsilon^{\mu \nu \alpha \beta} = L^{\mu}_{\delta}L^{\nu}_{\gamma}L^{\alpha}_{\theta}L^{\beta}_{\psi} \hat \epsilon^{\delta \gamma \theta \psi}$$

and somehow play around with the LHS to show it is equal to ##\epsilon^{\mu \nu \alpha \beta}##. Am I right ? Problem is I'm completely out of ideas.

Thanks

Ric