A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the position and orientation of the matter fields. … Continued
We discuss a coordinate-free approach to the geometry of computer vision problems. The technique we use to analyse the 3-dimensional transformations involved will be that of geometric algebra: a framework based on the algebras of Clifford and Grassmann. This is … Continued
Stationary vacuum solutions of Kerr-Schild type are analysed within the framework of gauge-theory gravity. The complex structure at the heart of these fields is shown to have a clear geometric origin, with the role of the unit imaginary fulfilled by … Continued
Kerr-Schild solutions to the vacuum Einstein equations are considered from the viewpoint of a gauge-theoretic formulation of gravity. This formulation employs the spacetime algebra (the Clifford algebra of spacetime), which offers a number of novel insights into the nature of … Continued
It is shown that higher-weighted representations of rotation groups can be constructed using multilinear functions in geometric algebra. Methods for obtaining the irreducible representations are found, and applied to the spatial rotation group, SO(3), and the proper Lorentz group, SO+(1,3). … Continued
The spin-torsion sector of a new gauge-theoretic formulation of gravity is analysed and the relationship to the Einstein-Cartan-Kibble-Sciama theory of gravity is discussed. The symmetries of the Riemann tensor and the conservation laws of the theory are derived. This formalism … Continued
We present a new, fully covariant and manifestly gauge-invariant expression for the temperature anisotropy in the cosmic microwave background radiation resulting from scalar perturbations. We pay particular attention to gauge issues such as the definition of the temperature perturbation and … Continued