4,221 research outputs found
Part II: Spacetime Algebra of Dirac Spinors
In "Part I: Vector Analysis of Spinors", the author studied the geometry of
two component spinors as points on the Riemann sphere in the geometric algebra
of three dimensional Euclidean space. Here, these ideas are generalized to
apply to four component Dirac spinors on the complex Riemann sphere in the
complexified geometric algebra of spacetime, which includes Lorentz
transformations. The development of generalized Pauli matrices eliminate the
need for the traditional Dirac gamma matrices. We give the discrete probability
distribution of measuring a spin 1/2 particle in an arbitrary spin state,
assuming that it was prepared in a given state immediately prior to the
measurement, independent of the inertial system in which measurements are made.
The Fierz identities between the physical observables of a Dirac spinor are
discussed.Comment: 21 pages, 3 figure
- …