  The microlocal space-time of extended hadrons, considered to be anisotropic
is specified here as a special Finsler space. For this space the classical
field equation is obtained from a property of the field on the neighbouring
points of the autoparallel curve. The quantum field equation has also been
derived for the bispinor field of a free lepton in this Finslerian microspace
through its quantum generalization below a fundamental length-scale. The
bispinor can be decomposed as a direct product of two spinsors, one depending
on the position coordinates and the other on the directional arguments of the
Finsler space. The former one represents the spinor of the macrospace, an
associated Riemannian space-time of the Finsler space, and satisfies the Dirac
equation. The directional variable-dependent spinor satisfies a different
equation which is solved here. This spinor-part of the bispinor field for a
constituent of the hadron can give rise to an additional quantum number for
generating the internal symmetry of hadrons. Also, it is seen that in the
process of separating the bispinor field and its equation an epoch-dependent
mass term arises. Although, this part of the particle-mass has no appreciable
contribution in the present era it was very significant for the very early
period of the universe after its creation. Finally, the field equations for a
particle in an external electromagnetic field for this Finslerian microlocal
space-time and its associated Riemannian macrospaces have been found.
