  Recently Weyl fermions have attracted increasing interest in condensed matter
physics due to their rich phenomenology originated from their nontrivial
monopole charges. Here we present a theory of real Dirac points that can be
understood as real monopoles in momentum space, serving as a real
generalization of Weyl fermions with the reality being endowed by the $PT$
symmetry. The real counterparts of topological features of Weyl semimetals,
such as Nielsen-Ninomiya no-go theorem, $2$D sub topological insulators and
Fermi arcs, are studied in the $PT$ symmetric Dirac semimetals, and the
underlying reality-dependent topological structures are discussed. In
particular, we construct a minimal model of the real Dirac semimetals based on
recently proposed cold atom experiments and quantum materials about $PT$
symmetric Dirac nodal line semimetals.
