  In Ref. \cite{Horava2005} Ho\v{r}ava suggested, that the multi - fermion
many-body system with topologically stable Fermi surfaces may effectively be
described (in a vicinity of the Fermi surface) by the theory with
coarse-grained fermions. The number of the components of these coarse-grained
fermions is reduced compared to the original system. Here we consider the $3+1$
D system and concentrate on the particular case when the Fermi surface has
co-dimension $p=3$, i.e. it represents the Fermi point in momentum space. First
we demonstrate explicitly that in agreement with Ho\v{r}ava conjecture, in the
vicinity of the Fermi point the original system is reduced to the model with
two - component Weyl spinors. Next, we generalize the construction of
Ho\v{r}ava to the situation, when the original $3+1$ D theory contains multi -
component Majorana spinors. In this case the system is also reduced to the
model of the two - component Weyl fermions in the vicinity of the topologically
stable Fermi point. Those fermions experience the emergent gauge field and the
gravitational field given by the emergent veirbein. Both these fields (the
emergent gauge field and the emergent gravitational field) originate from
certain collective excitations of the original system. We speculate, that the
given construction may be relevant for the high energy physics in the paradigm,
in which the Lorentz symmetry as well as the gravitational and gauge fields are
the emergent phenomena, i.e. they appear dynamically in the low energy
approximation of the underlined high energy theory.
