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Suppose we're trying to localize particle obeying relativistic wave equation in space. As we know, then pairs of particles and antiparticles will occur, unlike the situation with non-relativistic theory. From the other side, antiparticles are needed in Poincare-covariant theory for restoring the causality of the theory.

Therefore I want to ask: is there any direct relation between the Klein paradox and the causality?

As we know from the right results of relativistic quantum electrodynamics, we always deal with multi-particle systems and the "classical mechanical" results are inclusive QED pictures where a sum on soft photons is carried out. No wonder that Poincaré covariance is about relativistic systems with multi-particle contents. Soft photons have no threshold to be created/absorbed, massive particles have, but in a relativistic limit this threshold is negligible and a truly relativistic system is inevitably multi-particle, so is its mathematical description.

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