A major part of the research of the Geometric Algebra group has continued to be the development of applications of a new gauge theory of gravity (described in Lasenby, Doran & Gull (in press) and Doran, Lasenby & Gull, 1996b). The use of geometric algebra greatly facilitates calculations, and provides a deeper understanding of the matter and energy distributions in rotating strings (Doran, Lasenby & Gull, 1996a) and at the heart of a Kerr black hole (Doran, Lasenby & Gull, submitted).
A review of the group's work on electron physics has been published in Doran et al., (1995). Hestenes' original geometric interpretation of the Dirac wavefunction has been refined and extended to the multiparticle case. Applied to a neutron in a magnetic field, these ideas allow a causal, fully relativistic account of the measurement of spin (Challinor et al., 1996). It becomes clear that a non-uniform magnetic field acts as a spin polarizer, with the neutron spin eventually rotating to align parallel to, or opposed to, the applied field. A causal, fully relativistic account has also been given of the process of electron tunnelling (Challinor et al., in press), with new calculations showing that a particle wavepacket arrives earlier if it passes through a barrier compared to one travelling in free space. This result is in agreement with some recent experiments on photon tunnelling, and the causal approach shows graphically how apparent `faster than light' travel can occur without any need for actual superluminal velocities.
The geometric algebra approach to gravity was employed as a tool in Dabrowski
et al. (in press) and A.Lasenby et al. (in press), where photon
trajectories were calculated in order to find spectral lineshapes from iron
fluorescence in the accretion disk around a rotating (Kerr) black hole.
Comparing the results with the observed lineshape in MCG--6-30-15 yielded
strong evidence for the rotation rate of the hole being near the extreme limit
.
A series of lectures at a summer school in Banff were published as a book (Doran, Lasenby & Gull, 1996b), where the Cambridge group contributed 12 chapters. As well as describing the work on electron physics and gravitation, new results were given in the field of electromagnetism, robotics, computer vision and dynamics. These included a novel approach to the dynamics of elastic media, which uses the ideas developed in the gravity theory to handle arbitrarily large displacements. Further applications of geometric algebra to computer vision are contained in J.Lasenby et al. (in press).