  The disclination in Lorentz space-time is studied in detail by means of
topological properties of $\phi $-mapping. It is found the space-time
disclination can be described in term of a Dirac spinor. The size of the
disclination, which is proved to be the difference of two sets of su(2)% -like
monopoles expressed by two mixed spinors, is quantized topologically in terms
of topological invariants$-$winding number. The projection of space-time
disclination density along an antisymmetric tensor field is characterized by
Brouwer degree and Hopf index.
