  The geometrical underpinnings of a specific class of Dirac operators is
discussed. It is demonstrated how this class of Dirac operators allow to relate
various geometrical functionals like, for example, the Yang-Mills action and
the functional of non-linear $\sigma-$models (i.e. of (Dirac) harmonic maps).
These functionals are shown to be similar to the Einstein-Hilbert action with
cosmological constant (EHC). The EHC may thus be regarded as a "generic
functional". As a byproduct, the geometrical setup presented also allows to
avoid the issue of "fermion doubling" as usually encountered, for instance, in
the geometrical discussion of the Standard Model in terms of Dirac operators.
Furthermore, it is demonstrated how the geometrical setup presented allows to
derive the cosmological constant term of the EHC from the Einstein-Hilbert
functional and the action of a purely gauge coupling Higgs field.
