Shouldn't there be symmetry and unitarity given energy conservation? And quaternions express this with rotations in SO(3), but is there a better model than quat

Shouldn't there be symmetry and unitarity given energy conservation? And quaternions express this with rotations in SO(3), but is there a better model than quaternions for EM field theory since 1861? -1 = i^2 = j^2 = k^2 q = a + bi + cj + dk q = a + xi + yj + zk (Edit) Quaternions and spatial rotation: https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotati... QED: Quantum electrodynamics: https://en.wikipedia.org/wiki/Quantum_electrodynamics https://en.wikipedia.org/wiki/Quantum_electrodynamics : > Mathematically, QED is an abelian gauge theory with the symmetry group U(1), defined on Minkowski space (flat spacetime). The gauge field, which mediates the interaction between the charged spin-1/2 fields, is the electromagnetic field. The QED Lagrangian for a spin-1/2 field interacting with the electromagnetic field in natural units gives rise to the action [...] And QED is the basis for the Standard Model of particle physics and for some theories of n-body quantum gravity.