  We study the "Lie Algebra" of the group of Gauge Transformations of
Space-time. We obtain topological invariants arising from this Lie Algebra. Our
methods give us fresh mathematical points of view on Lorentz Transformations,
orientation conventions, the Doppler shift, Pauli matrices , Electro-Magnetic
Duality Rotation, Poynting vectors, and the Energy Momentum Tensor $T$ .
