  We compute gauge theories of the Lorentz group. We discuss non-interacting,
and interacting fermionic systems. The interacting system combines a local with
a global Lorentz group, i.e, discusses a $SO(3,1)_{l}\times
SO(3,1)_{g}$-theory. We compute the equations of motion and conservation laws
for the fermionic matter current. The core of our work is the prediction of
some new form of monopoles we call 'Dirac-Clifford-'t Hooft-Polyakov'-monopole.
It resides in a state similar to color-flavor locking. Dirac-Clifford-'t
Hooft-Polyakov-monopoles are invariant under global Lorentz transformations and
are predicted to form vortices. The theory is renormalizable, since all
Goldstone-Nambu modes are converted into massive vector gauge fields.
