Angular momentum gauge invariant

This expression of K is gauge-invariant, and both of the first and the second terms on the right-hand side of Eq. (10) are independent of the choice of body frame. The former vanishes if and only if the total angular momentum L is zero [cf. Eq. (5)]. The metric tensor g in Eq. (11) is also gauge-invariant and is the true metric appropriate for the description of internal motions in polyatomic molecules. 

The most significant difference of Dirac s results from those of the non-relativistic Pauli equation is that the orbital angular momentum and spin of an electron in a central field are no longer separate constants of the motion. Only the components of J = L - - S and J, which commute with the Hamiltonian, emerge as conserved quantities [1]. Dirac s equation, extended to general relativity by the method of projective relativity [2], automatically ensures invariance with respect to gauge, coordinate and spinor transformations, but has never been solved in this form. 

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