Classical and Quantum Dynamics in a Black Hole Background
Lecture delivered in the Cavendish Laboratory, Cambridge, 2004. PDF
New Techniques for Analysing Axisymmetric Gravitational Systems. 1. Vacuum Fields
A new framework for analysing the gravitational fields in a stationary, axisymmetric configuration is introduced. The method is used to construct a complete set of field equations for the vacuum region outside a rotating source. These equations are under-determined. Restricting … Continued
Applications of Geometric Algebra in Electromagnetism, Quantum Mechanics and Gravity
We review the applications of geometric algebra geometric algebra in electromagnetism, gravitation and multiparticle quantum systems. We discuss a gauge theory formulation of gravity and its implementation in geometric algebra, and apply this to the fermion bound state problem in … Continued
Modelling the Cosmos
Anthony Lasenby’s keynote address at the SIGGRAPH 2003 conference in San Diego. PPT Movies
Perturbation Theory Calculation of the Black Hole Elastic Scattering Cross Section
The differential cross section for scattering of a Dirac particle in a black hole background is found. The result is the gravitational analog of the Mott formula for scattering in a Coulomb background. The equivalence principle is neatly embodied in … Continued
State-Space Based Approach to Particle Creation in Spatially Uniform Electric Fields
Our formalism described recently in (Dolby et al, hep-th/0103228) is applied to the study of particle creation in spatially uniform electric fields, concentrating on the cases of a time-invariant electric field and a so-called `adiabatic’ electric field. Several problems are … Continued
Conformal Geometry, Euclidean Space and Geometric Algebra
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to programming complicated geometrical operations. But there is a fundamental … Continued
Analysis of 1 and 2 Particle Quantum Systems using Geometric Algebra
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this entanglement … Continued
Interaction and Entanglement in the Multiparticle Spacetime Algebra
The multiparticle spacetime algebra (MSTA) is an extension of Dirac theory to a multiparticle setting, which was first studied by Doran, Gull and Lasenby. The geometric interpretation of this algebra, which it inherits from its one-particle factors, possesses a number … Continued
Jet Bundles and the Formal Theory of Partial Differential Equations
Systems of partial differential equations lie at the heart of physics. Despite this, the general theory of these systems has remained rather obscure in comparison to numerical approaches such as finite element models and various other discretisation schemes. There are, … Continued