  Causal fermion systems incorporate local gauge symmetry in the sense that the
Lagrangian and all inherent structures are invariant under local phase
transformations of the physical wave functions. In the present paper it is
explained and worked out in detail that, despite this local gauge freedom, the
structures of a causal fermion system give rise to distinguished gauges where
the local gauge freedom is fixed completely up to global gauge transformations.
The main method is to use spectral and polar decompositions of operators on
Hilbert spaces and on indefinite inner product spaces. We also introduce and
make use of a Riemannian metric which is induced on the manifold of all regular
correlation operators by the Hilbert-Schmidt scalar product. Gaussian
coordinate systems corresponding to this Riemannian metric are constructed.
Moreover, we work with so-called wave charts where the physical wave functions
are used as coordinates. Our constructions and results are illustrated in the
example of Dirac sea configurations in finite and infinite spatial volume.
