Might it be $L^{\nu}=(0, \vec L)$, where $\vec L=\int\,\vec p \times \vec r\,dV$ is the three dimensional angular momentum? But latter would hold only for low angular velocities. What is the angular momentum vector in Special Relativity? We must use the four dimensional vectors. But the product $\epsilon_{\nu \mu \alpha \beta}\,p^{\alpha}\,x^{\beta}$ is not a vector, but the tensor.
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1Have you looked at the Wikipedia article on relativistic angular momentum? – John Rennie May 01 '18 at 06:41
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No, I was sure that nobody knows. But thank you. – Dmitri Martila May 01 '18 at 07:01