Representations of tensor rotations and the geometry of spin 1/2

Abstract

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 biggest 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.