Clifford Algebra and the Interpretation of Quantum Mechanics

Abstract

The Dirac theory has a hidden geometric structure. This talk traces the concep- tual steps taken to uncover that structure and points out significant implications for the interpre- tation of quantum mechanics. The unit imaginary in the Dirac equation is shown to represent the generator of rotations in a spacelike plane related to the spin. This implies a geometric interpreta- tion for the generator of electromagnetic gauge transformations as well as for the entire electroweak gauge group of theWeinberg-Salam model. The geometric structure also helps to reveal closer con- nections to classical theory than hitherto suspected, including exact classical solutions of the Dirac equation.