  In the present work, we give a phenomenological theory of the monolayer
graphene where two worlds quantum and classical meet together and complete each
other in the most natural way. It appears that the graphene is the unique
material where this complementarity could be explained in an effective way due
to its exceptional band structure properties. We introduce the electron
mass-vortex representation and we define surface tension excitation states in
the monolayer graphene. By abstracting from the usual band energy dispersion we
calculate the band mass of the electrons at the Dirac point by introducing the
mathematical mass-dispersion relation. As a result, we obtain the Dirac energy
dispersion in monolayer graphene from the classical Newton law. Within the
semiclassical theory, we show the presence of the surface spin tension
vectorial field which, possibly, closely relates the surface tension and spin
tension states on the helical surface. We calculate the surface tension related
with the electron band mass-vortex formation at the Dirac's point and we
predict accurately the surface tension value related to the excitonic binding
at the Dirac point as being formed from the electron and hole band
mass-vortices. Moreover, we give the solution to a long-standing problem in the
spin group theory and we construct an example which shows, phenomenologically,
that the manifolds on $\rm S^{(6)}$ are not integrable. The principal reason
for this is attributed to the irreducibility of the spinorial group $\rm
Spin(6)^{\rm R}$ at the Dirac's point, due to the band mass formation via
gravitational field.
