>>13829917>you cant embed a lorentzian manifold into a riemannian oneFor definition of the variables which are invariant relative to diffeomorphisms,
and thereby, elimination of gauge arbitrariness in solutions
of equations of the theory, it is necessary to separate general coordinate
transformations (which play the role of gauge ones) from the Lorentzian
ones. The solution of the problem of separation of general coordinate
transformations from relativistic transformations of systems of reference
was suggested by Fock [14] in his paper on introduction of spinor fields
in the Riemannian space. In fact, instead of a metric tensor, Fock introduced
tetrads defined as “square root” of the metric tensor, with two indices.
One index relates to Riemannian space, being the base space, and
the second – to a tangent Minkowskian space. Tetrad components are
coefficients of decomposition of Cartan’s forms via differentials of coordi-
nate space. These differential forms, by definition, are invariants relative
to general coordinate transformations, and have a meaning as measurable
geometric values of physical space, and integrable non-invariant differentials
of coordinate space considered as auxiliary mathematical values of
the kind of electromagnetic potentials in electrodynamics.
