Applying the spacetime geometric algebra in magnetized plasma electromagnetism: Is it only a matter of beauty?

Geometric algebras {GAs) offer an elegant way to describe rotations on Bloch hyperspheres. The latter are synonymous to the so-called qubits in the realm of Quantum Information and their implementation via Quantum Computing techniques. The question that naturally arises is if elegance is a high price to pay in adapting the geometric approach in a problem that cubits are involved. However, it is generally accepted in the scientific community that GAs are, by far, the easiest way to describe rotations in space and in higher dimensions. This is become more obvious if one deals with such transformations in the realm of special relativity and the associated Lorentz transformations in four dimensional Minkowskian spacetime.