Supervisor: Dr Timothy Walton
The natural mathematical language to discuss the differential properties of spacetime tensor fields arising in general relativistic descriptions of physical phenomena is in terms of differential forms and their associated exterior calculus. It can be shown that, given a metric tensor field, there exists an isomorphism between the exterior and Clifford algebras on spacetime. This project will exploit this isomorphism to formulate the “Dirac equation” describing the motion of spin-1/2 particles (such as electrons) and its spinor solutions in terms of inhomogeneous differential forms. A coupling of such spinor solutions, in particular those possessing a chiral nature, to gravitation will influence the motion of massive test particles. We can use this formulation to model observable properties of pulsars and the formation of spiral galaxies.