Introduction.- Comparison between Complex and Real Algebraic Languages.- The Clifford Algebra Associated with the Minkowski Space-Time M.- Comparison between Real and Complex Languages.- The U(1) Gauge in Complex and Real Languages - Geometrical Properties and Relation with the Spin and the Energy of a Particle of Spin 1/2.- Geometrical Properties of the U(1) Gauge.- Relation between the U(1) Gauge, the Spin and the Energyof a Particle of Spin 1/2.- Geometrical Properties of the Dirac Theory of the Electron.- The Dirac Theory of the Electron in the Real Language.- The Invariant Form of the Dirac Equation and Invariant Properties of the Dirac Theory.- The U(2) Gauge and the Yang-Mills Theory in Complex and Real Languages.- Geometrical Properties of the SU(2) _ U(1) Gauge.- The Glashow-Salam-Weinberg Electroweak Theory.- The Electroweak Theory in STA. Global Presentation.- The Electroweak Theory in STA. Local Presentation.- On a Change of SU(3) into Three SU(2)XU(1).- A Change of SU(3) into Three SU(2)_U(1).

This book continues the fundamental work of Arnold Sommerfeld and David Hestenes formulating theoretical physics in terms of Minkowski space-time geometry. We see how the standard matrix version of the Dirac equation can be reformulated in terms of a real space-time algebra, thus revealing a geometric meaning for the "number i" in quantum mechanics. Next, it is examined in some detail how electroweak theory can be integrated into the Dirac theory and this way interpreted in terms of space-time geometry. Finally, some implications for quantum electrodynamics are considered. The presentation of real quantum electromagnetism is expressed in an addendum. The book covers both the use of the complex and the real languages and allows the reader acquainted with the first language to make a step by step translation to the second one.