Achronal localization and representation of the causal logic from a conserved current, application to the massive scalar boson

Covariant achronal localizations are gained out of covariant conserved currents computing their flux passing through achronal surfaces. This general method applies to the probability density currents with causal kernel regarding the massive scalar boson. Due to the one-to-one correspondence between (covariant) achronal localizations and (covariant) representations of the causal logic thus, apparently for the first time, a covariant representation of the causal logic for an elementary relativistic quantum mechanical system has been achieved. Similarly one derives the covariant family of representations of the causal logic related to the stress energy tensor of the massive scalar boson. While reaching this result the divergence theorem is proven for open sets with almost Lipschitz boundary.