  Making use of the real sl(2,R) Lie group algebra generating a spin 1/2 Lie
group allows to create an explicitly given Lorentz invariant fermion wave. As
the generators are real valued they can be interpreted as a deformation tensor
in particular as a deformation tensor of space. Therefore, it is possible to
model a heuristic purely geometric representation of spin 1/2 in Minkowski
space. However the bigger surprise is that this wave has the space-time
structure of gravitational waves, which are understood to be spin 2 waves.
Given that the uniqueness of angular momentum representations still holds, the
examination of tensor rotations reveals the existence of different
representations of tensor rotations with a different angular parameter due to
an unaccounted basic symmetry of symmetric tensors, where the spin 1/2
representation is a specific representation of tensor rotations corresponding
to the quantum theoretical approach. The seeming contradiction is fully
resolved and allows in addition to understand the notion of different
representations of spin in tensors, again related to different representations
of the tensor.
