Quantum Mechanics in the Geometry of Space-Time

Abstract

This book continues the fundamental work of Arnold Sommerfeld andDavid Hestenes formulating theoretical physics in terms of Minkowskispace-time geometry. We see how the standard matrix version of theDirac equation can be reformulated in terms of a real space-timealgebra, thus revealing a geometric meaning for the “number i” inquantum mechanics. Next, it is examined in some detail how electroweaktheory can be integrated into the Dirac theory and this way interpretedin terms of space-time geometry. Finally, some implications for quantumelectrodynamics are considered.The presentation of real quantum electromagnetismis expressed in an addendum. The book covers both the use of thecomplex and the real languages and allows the reader acquainted withthe first language to make a step by step translation to the secondone.