What is potential energy in special relativity?

I know what is rest energy $E_0=m_0 c^2$, total energy $E=\gamma E_0$, kinetic energy $E- E_0=(\gamma-1) E_0$, and momentum $p=\gamma m_0 c$. But what is potential energy in special relativity?

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The same thing it is in Newtonian mechanics. The expressions you are working with are for a free particle. If you put it in a potential the energy has another contributions. – dmckee Mar 4 '13 at 0:06

If the source does not move, it creates a static electromagnetic field for a probe charge and it has classical interpretation, kind of $V(\vec{r}_1-\vec{r}_2)$. If the source moves, its electromagnetic field becomes retarded, so the third Newton law may be violated. In that case there is no potential energy of interaction of particles $V(\vec{r}_1-\vec{r}_2)$, but there is an interaction of a particle with an "external" electromagnetic field $q_i \varphi(\vec{r}_i,t)$ that depends on time explicitly.