Relativistic generalization of the Born rule

Abstract

We have shown that the Born rule $(\rho=|\psi|^{2})$ is inconsistent with Lorentz symmetry of the Salpeter equation (square root Klein-Gordon equation). So we find relativistic modification of the Born rule as $\rho=\frac{1}{2mc^{2}}(|\sqrt{\widehat{H}-mc^{2}}\psi|^{2}+|\sqrt{\widehat{H}+mc^{2}}\psi|^{2})$ , which is consistent with Lorentz symmetry of this equation