  The winding numbers for the even d+1 spacetime dimensional Weyl Hamiltonians
are calculated in terms of the related Green's functions. It is shown that
these winding numbers result in the divergence of the Dirac monopole fields,
hence they are equal to the unit topological charge. It is demonstrated that
the winding numbers are also equal to the Chern numbers which are expressed as
the integral of the Berry field strength. Explicit calculations are presented
for the 3+1 and 5+1 dimensional cases. Relevance of these topological
invariants for the physical systems like the semiclassical chiral kinetic
theory are discussed.
