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However, the Hamiltonian operator is got from rewriting the Dirac equation in a form adapted to a particular reference frame, or class of coordinate systems. That rewriting does not commute with changing the tetrad field $(u_\\alpha)$. The data of a reference frame F fixes a four-velocity field $v$, and also fixes a rotation-rate field $\\Mat{\\Omega}$. It is natural to impose that $u_0=v$. 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