Publications
Below is a list of publications by the Geometric
Algebra Research Group. Click on the title of a paper to read its
abstract. PDF and Postscript files of most of the papers are available.
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2005
Anthony Lasenby, Chris Doran and Reece Heineke
Analytic solutions
to Riemann-squared gravity with background isotropic torsion
gr-qc/0509014
Alejandro Caceres and Chris Doran
Minimax determination
of the energy spectrum of the Dirac equation in a Schwarzschild
background
Phys. Rev. A (to appear)
Anthony Lasenby and Chris Doran
Closed Universes, de
Sitter Space and Inflation
Phys.Rev. D 71, 063502 (2005)
Anthony Lasenby
Conformal Geometry and the
Universe
Phil.Trans.R.Soc.Lond.A (to appear)
Chris Doran and Anthony Lasenby
Integral equations,
Kerr-Schild fields and gravitational sources
gr-qc/0404081
Chris Doran, Anthony Lasenby, Sam Dolan and Ian
Hinder
Fermion absorption cross
section of a Schwarzschild black hole
Phys.Rev. D 71, 124020 (2005)
Rich Wareham, Jonathan Cameron, and Joan Lasenby
Applications of Conformal Geometric
Algebra in Computer Vision and Graphics
H. Li, P. J. Olver and G. Sommer (Eds.): IWMM 2004, LNCS 3519, pp.
329–349, 2005. Springer-Verlag (2005)
Anthony Lasenby
Recent Applications of
Conformal Geometric Algebra
H. Li, P. J. Olver and G. Sommer (Eds.): IWMM 2004, LNCS 3519 Springer-Verlag
(2005)
Suguru Furuta
Control and Measurement
of Quantum Spins: Theory and Simulations
PhD Thesis (2005)
2004
Anthony Lasenby and Chris Doran
Conformal models of
de Sitter space, initial conditions for inflation and the CMB
Proceedings 'Phi in the Sky', Porto, 2004
Chris Doran
Circle and sphere
blending with conformal geometric algebra
cs.CG/0310017
Timothy Havel and Chris Doran
A Bloch-Sphere-Type Model
for Two Qubits in the Geometric Algebra of a 6-D Euclidean Vector
Space
Proc. SPIE, vol. 5436 (Quantum Information and Computation II, E
Donkor, A. R. Pirich & H. E. Brandt, eds.), pp. 93-106 (2004)
Suguru Furuta, Crispin Barnes and Chris Doran
Single-qubit gates and
measurements in the surface acoustic wave quantum computer
Phys. Rev. B 70, 205320 (2004)
2003
Chris Doran and Anthony Lasenby
Geometric
Algebra for Physicists
Cambridge University Press (2003)
Chris Doran and Anthony Lasenby
New Techniques for Analysing
Axisymmetric Gravitational Systems. 1. Vacuum Fields
Class.Quant.Grav. 20, 1077-1102 (2003)
T.F. Havel, C.J.L. Doran and S. Furuta
Density Operators in
the Multiparticle Spacetime Algebra
Proc. Royal. Soc. (to appear)
A.N. Lasenby, C.J.L. Doran and E. Arcaute
Applications of Geometric
Algebra in Electromagnetism, Quantum Mechanics and Gravity
In R. Ablamowicz, ed. Sixth International Conference on Clifford
Algebras and their Applications, Tennessee 2002, p. 467, Birkhauser
(2003)
2002
Anthony Lasenby, Chris Doran, Jonathan Pritchard,
Alejandro Caceres and Sam Dolan
Bound States and Decay
Times of Fermions in a Schwarzschild Black Hole Background
gr-qc/0209090
C.J.L. Doran and A.N. Lasenby
Perturbation Theory Calculation
of the Black Hole Elastic Scattering Cross Section
Phys. Rev. D, 66(2), 024006 (2002)
C.E. Dolby and S.F. Gull
State-Space Based
Approach to Particle Creation in Spatially Uniform Electric Fields
Annals Phys. 297, 315-343 (2002)
Chris Doran, Anthony Lasenby and Joan Lasenby
Conformal Geometry, Euclidean
Space and Geometric Algebra
In J. Winkler ed Uncertainty in Geometric Computations, p.41
Kluwer (2002)
R.F. Parker and C.J.L. Doran
Analysis of 1 and 2 Particle
Quantum Systems using Geometric Algebra
In C. Doran, L. Dorst and J. Lasenby eds. Applied Geometrical
Alegbras in computer Science and Engineering, AGACSE 2001, p.213,
Birkhauser (2002).
T.F. Havel and C.J.L. Doran
Interaction and Entanglement
in the Multiparticle Spacetime Algebra
In C. Doran, L. Dorst and J. Lasenby eds. Applied Geometrical
Alegbras in computer Science and Engineering, AGACSE 2001, p.
227, Birkhauser (2002)
R.C.D. Baker and C.J.L. Doran
Jet Bundles and the Formal Theory
of Partial Differential Equations
In C. Doran, L. Dorst and J. Lasenby eds. Applied Geometrical
Alegbras in computer Science and Engineering, AGACSE 2001, p.
133, Birkhauser (2002)
Anthony Lasenby and Chris Doran
Geometric Algebra, Dirac
Wavefunctions and Black Holes
In P.G. Bergmann and V. de Sabbata eds, Advances in the Interplay
Between Quantum and Gravity Physics, Kluwer 2002, 251-283
2001
C.J.L. Doran et. al
Geometric
Algebra
Course notes for the 28th International Conference on Computer Graphics
and Interactive
Techniques, SIGGRAPH 2001, Course 53.
A. Lewis, C.J.L. Doran and A.N. Lasenby.
Electron scattering without
spin sums.
Int. J. Theor. Phys. 40(1) (2001)
Carl Dolby
A state-space based approach
to quantum field theory in classical background fields
PhD Thesis (2001)
C.E. Dolby and S.F. Gull
New approach to quantum field
theory for arbitrary observers in electromagnetic backgrounds
Annals of Physics 293, 189-214 (2001)
C.E. Dolby and S.F. Gull
On radar time and the twin
`paradox'
Am. J. Phys. 69, 1257-1261 (2001)
Anthony Lasenby and Joan Lasenby
Surface Evolution and Representation
using Geometric Algebra
In Roberto Cipolla and Ralph Martin eds. The Mathematics of Surfaces
IX: Proceedings of the ninth IMA conference on the mathematics of
surfaces, p144-168, Springer, London (2001)
2000
C.J.L. Doran
A new form of the Kerr solution
Phys. Rev. D 61(6), 067503 (2000)
C.J.L. Doran et. al
Geometric
Algebra: New Foundations, New Insights
Course notes for the 27th International Conference on Computer Graphics
and Interactive Techniques, SIGGRAPH 2000, Course
C.J.L. Doran
Bayesian inference and geometric
algebra: an application to camera localization
In: E. Bayro and G. Sobczyk eds. Geometric algebra: a geometric
approach to computer vision, neural and quantum computing, robotics
and engineering. Birkhauser, 172 (2000)
J. Lasenby and A. Stevenson
Using geometric algebra in
optical motion capture
In: E. Bayro and G. Sobczyk eds. Geometric algebra: a geometric
approach to computer vision, neural and quantum computing, robotics
and engineering. Birkhauser (2000)
A.N. Lasenby and J Lasenby
Applications of Geometric
Algebra in Physics and Links with Engineering
In: E. Bayro and G. Sobczyk eds. Geometric algebra: a geometric
approach to computer vision, neural and quantum computing, robotics
and engineering. Birkhauser (2000)
J. Lasenby, A.N. Lasenby and C.J.L. Doran
A unified mathematical language
for physics and engineering in the 21st century
Phil. Trans. R. Soc. Lond. A 358, 21-39 (2000)
T.F. Havel and C.J.L. Doran
Geometric algebra in quantum
information processing
In S. Lomonaco, ed. Quantum Computation and Quantum Information
Science. AMS Contemporary Math series (2000). quant-ph/0004031
A. Lewis, C. Doran and A.N. Lasenby.
Quadratic Lagrangians and
topology in gauge theory gravity
General Rel. Grav. 32(1), 161 (2000)
A. Lewis, A.N. Lasenby and C.J.L. Doran.
Electron scattering in
the spacetime algebra
R. Ablamowicz and B. Fauser eds., 5th International Conference
on Applications of Clifford Algebra, Ixtapa, Mexico 1999, 49-71
(2000)
1999
S.S. Somaroo, A.N. Lasenby and C.J.L. Doran
Geometric algebra and
the causal approach to multiparticle quantum mechanics
J.
Math. Phys. 40(7), 3327-3340 (1999).
A.N. Lasenby, C.J.L. Doran, M.P. Hobson, Y.Dabrowski and A.D.
Challinor
Microwave Background
Anisotropies and Nonlinear Structures I. Improved Theoretical Models.
Mon. Not. R. Astron. Soc. 302, 748--756 (1999).
Y.Dabrowski, M.P. Hobson, A.N. Lasenby and C.J.L. Doran.
Microwave Background
Anisotropies and Nonlinear Structures II. Numerical computations.
Mon. Not. R. Astron. Soc. 302, 757--770 (1999).
1998
A. N. Lasenby, C. J. L. Doran and S. F. Gull.
Gravity, gauge theories and
geometric algebra
Phil. Trans. R. Soc. Lond. A356, 487-582 (1998).
J. Lasenby, W. J. Fitzgerald, C. J. L. Doran and A. N. Lasenby.
New Geometric Methods for Computer
Vision
Int. J. Comp. Vision 36(3), p. 191-213 (1998).
C. J. L. Doran
Integral equations and
Kerr-Schild fields I. Spherically-symmetric fields
Preprint (1998)
C. J. L. Doran, A. N. Lasenby and S. F. Gull
Integral equations and
Kerr-Schild fields II. The Kerr solution
Preprint (1998)
M. A. J. Ashdown, S. S. Somaroo, S. F. Gull, C. J. L. Doran and
A. N. Lasenby
Multilinear Representations
of Rotation Groups within Geometric Algebra
J. Math. Phys. 39(3), 1566-1588 (1998).
C.J.L Doran, A.N. Lasenby, A.D. Challinor and S.F. Gull
Effects of spin-torsion
in gauge theory gravity
J. Math. Phys. 39(6), 3303--3321 (1998).
A. D. Challinor and A. N. Lasenby
A covariant and gauge-invariant
analysis of cosmic microwave background anisotropies from scalar
perturbations.
Phys.Rev. D 58 (1998)
1997
A. D. Challinor, A. N. Lasenby, S. S. Somaroo, C. J. L. Doran and
S. F. Gull.
Tunnelling times of
electrons
Phys. Lett. A, 227, 143-152 (1997).
A.D. Challinor, A.N. Lasenby, C.J.L. Doran and S.F. Gull
Massive, non-ghost solutions
for the Dirac field coupled self-consistently to gravity
General Rel. Grav. 29, 1527 (1997).
A. N. Lasenby, C. J. L. Doran, Y. Dabrowski and A. D. Challinor.
Rotating astrophysical
systems and a gauge theory approach to gravity
In N. Sanchez and A. Zichini, editors, Current Topics in Astrofundamental
Physics, Erice 1996. (World Scientific Publishing Co., 1997)p.
380-403.
J. Lasenby, E. Bayro-Corrochano, A. Lasenby and G. Sommer.
A new framework for the
computation of invariants and multiple view constraints in computer
vision
Proceedings of the International Conference on Image Processing
(ICIP), 1996, (1997).
Jeff Tomasi
Cylindrically symmetric
systems in gauge theory gravity
Masters Thesis
1996
Chris Doran, Anthony Lasenby, Stephen Gull, Shyamal Somaroo and
Anthony Challinor.
Spacetime Algebra and Electron
Physics
In P. W. Hawkes, editor, Advances in Imaging and Electron Physics,
Vol. 95, p. 271-386 (Academic Press, 1996).
A. N. Lasenby, C. J. L. Doran and S. F. Gull.
Lectures in Geometric
Algebra
In W. E. Baylis, editor, Clifford (Geometric) Algebras with Applications
to Physics, Mathematics and Engineering. (Birkhäuser Boston,
1996).
J. Lasenby.
Geometric algebra:
applications in engineering
In W. E. Baylis, editor, Clifford (Geometric) Algebras with Applications
to Physics, Mathematics and Engineering. (Birkhäuser Boston,
1996).
A. D. Challinor, A. N. Lasenby, S. F. Gull and C. J. L. Doran.
A relativistic, causal account
of spin measurement
Phys. Lett. A 218, 128-138 (1996).
S. S. Somaroo.
Applications of the Geometric
Algebra to Relativistic Quantum Theory
Ph.D. thesis, University of Cambridge (1996).
S. F. Gull, A. N. Lasenby and C. J. L. Doran
Geometric algebra,
spacetime physics and gravitation.
In O. Lahav, E. Terlevich and R. J. Terlevich, editors, Gravitational
Dynamics, (Cambridge University Press, 1996), pp. 171-180.
C. J. L. Doran, A. N. Lasenby and S. F. Gull.
The physics of rotating cylindrical
strings
Phys. Rev. D 54(10), 6021-6031 (1996).
J. Lasenby, E. Bayro-Corrochano, A.N. Lasenby and G. Sommer.
Geometric Algebra: a Framework
for Computing Invariants in Computer Vision
Proceedings of the International Conference on Pattern Recognition
(ICPR '96), Vienna.
E. Bayro-Corrochano, J. Lasenby and G. Sommer.
Geometric Algebra: a framework
for computing point and line correspondences and projective structure
using n uncalibrated cameras
Proceedings of the International Conference on Pattern Recognition
(ICPR '96), Vienna.
1995
A. N. Lasenby, C. J. L. Doran and S. F. Gull.
Astrophysical and Cosmological
Consequences of a Gauge Theory of Gravity
In N. Sanchez and A. Zichichi, eds. Advances in Astrofundamental
Physics. Erice 1994 (World Scientific Publishing Co., 1995),
p. 359-401.
1994
C J. L. Doran.
Geometric Algebra and its
Application to Mathematical Physics
Ph.D. thesis, University of Cambridge (1994).
1993
C. J. L. Doran, A. N. Lasenby and S. F. Gull.
Grassmann Mechanics, Multivector
Derivatives and Geometric Algebra
In Z. Oziewicz, A. Borowiec and B. Jancewicz, editors, Spinors,
Twistors, Clifford Algebras and Quantum Deformations (Kluwer
Academic, Dordrecht, 1993), p. 215-226.
A. N. Lasenby, C. J. L. Doran and S. F. Gull.
2-spinors, Twistors and
Supersymmetry in the Spacetime Algebra
In Z. Oziewicz, A. Borowiec and B. Jancewicz, editors, Spinors,
Twistors, Clifford Algebras and Quantum Deformations (Kluwer
Academic, Dordrecht, 1993), p.233-245.
A. N. Lasenby, C. J. L. Doran and S. F. Gull.
Grassmann Calculus, Pseudoclassical
Mechanics and Geometric Algebra
J. Math. Phys. 34(8), 3683-3712 (1993).
C. J. L. Doran, D. Hestenes, F. Sommen and N. van Acker.
Lie Groups as Spin Groups
J. Math. Phys. 34(8), 3642-3669 (1993).
S. F. Gull, A. N. Lasenby and C. J. L. Doran.
Imaginary Numbers are not
Real - the Geometric Algebra of Spacetime
Found. Phys. 23(9), 1175-1201 (1993)
C. J. L. Doran, A. N. Lasenby and S. F. Gull.
States and Operators in the Spacetime
Algebra
Found. Phys. 23(9), 1239-1264 (1993)
A. N. Lasenby, C. J. L. Doran and S. F. Gull.
A Multivector Derivative Approach
to Lagrangian Field Theory
Found. Phys. 23(10), 1295-1327 (1993)
S. F. Gull, A. N. Lasenby and C. J. L. Doran.
Electron Paths, Tunnelling
and Diffraction in the Spacetime Algebra
Found. Phys. 23(10), 1329-1356 (1993)
C. J. L. Doran, A. N. Lasenby and S. F. Gull.
Gravity as a Gauge Theory
in the Spacetime Algebra
In F. Brackx and R. Delanghe, editors, Clifford Algebras and
their Applications in Mathematical Physics. Deinze 1993 (Kluwer
Academic, Dordrecht, 1993), p. 375-385.
A. N. Lasenby, C. J. L. Doran and S. F. Gull.
Cosmological Consequences
of a Flat-Space Theory of Gravity
In F. Brackx and R. Delanghe, editors, Clifford Algebras and
their Applications in Mathematical Physics. Deinze 1993 (Kluwer
Academic, Dordrecht, 1993), p. 387-396.
1992
1991
S. F. Gull.
Charged Particles at Potential
Steps
In A. Weingartshofer and D. Hestenes, editors, The Electron
(Kluwer Academic, Dordrecht, 1991), p. 37-48.
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