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In scattering theory, one can form a lorentz invariant quantity by $\epsilon_{\mu 1 2\nu}P^{\mu}_{1}P^{\nu}_{2}$ which is really $1\otimes 1$ 's spin 0 state. Is there such a kind of argument to show $\epsilon_{\alpha\beta\mu\nu}$ is also invariant under lorentz transformation without showing the determinant of lorentz transformation being 1. I just want a fancier proof of this.

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