Books
Geometric Algebra for Physicists
Chris Doran and Anthony Lasenby
Cambridge University Press, 2003.
Applications of
Geometric Algebra in Computer Science and Engineering
Leo Dorst, Chris Doran and Joan Lasenby
Birkhauser, 2002.
Geometric
Algebra
C.J.L. Doran et. al
Course notes for the 28th International Conference on Computer Graphics
and Interactive
Techniques, SIGGRAPH 2001, Course 53.
Geometric
Algebra: New Foundations, New Insights
C.J.L. Doran et. al
Course notes for the 27th International Conference on Computer Graphics
and Interactive Techniques, SIGGRAPH 2000, Course
Geometric
Algebra and its Application to Mathematical Physics
C J. L. Doran
Ph.D. thesis, University of Cambridge (1994)
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In Press / Submitted
Anthony Lasenby, Chris Doran and Reece Heineke
Analytic
solutions to Riemann-squared gravity with background isotropic torsion
gr-qc/0509014
Elsa Arcaute, Anthony Lasenby and Chris Doran
A representation of twistors within geometric (Clifford) algebra
Submitted to J. Phys A.
Chris Doran and Anthony Lasenby
Integral equations, Kerr-Schild fields and gravitational sources
gr-qc/0404081
Circle and sphere
blending with conformal geometric algebra
Chris Doran
Submitted to: Computer Aided Geometric Design
Density
Operators in the Multiparticle Spacetime Algebra
T.F. Havel, C.J.L. Doran and S. Furuta
Proc. Royal. Soc., to appear (2006)
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Journal Articles
Fermion scattering
by a Schwarzschild black hole
Sam Dolan, Chris Doran, and Anthony Lasenby
Phys. Rev. D 74, 064005 (2006)
Bound
States and Decay Times of Fermions in a Schwarzschild Black Hole Background
Anthony Lasenby, Chris Doran, Jonathan Pritchard, Alejandro Caceres and
Sam Dolan
Phys. Rev. D 72, 105014 (2005)
Alejandro Caceres and Chris Doran
Minimax determination
of the energy spectrum of the Dirac equation in a Schwarzschild background
Phys. Rev. A 72, 022103 (2005)
Chris Doran, Anthony Lasenby, Sam Dolan and Ian Hinder
Fermion absorption
cross section of a Schwarzschild black hole
Phys.Rev. D 71, 124020 (2005)
Closed Universes,
de Sitter Space and Inflation
A.N. Lasenby and C.J.L. Doran
Phys.Rev. D 71, 063502 (2005)
Single-qubit
gates and measurements in the surface acoustic wave quantum computer
Suguru Furuta, Crispin Barnes and Chris Doran
Phys. Rev. B 70, 205320 (2004)
New
Techniques for Analysing Axisymmetric Gravitational Systems. 1 Vacuum
Fields
Chris Doran and Anthony Lasenby
Classical and Quantum Gravity, 20(6), 1077-1101
(2003)
gr-qc/0211070
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)
gr-qc/0106039
Electron
scattering without spin sums
A. Lewis, C.J.L. Doran and A.N. Lasenby
Int. J. Theor. Phys. 40(1) (2001)
New
form of the Kerr solution
C.J.L. Doran
Phys. Rev. D 61(6), 067503 (2000)
A
unified mathematical language for physics and engineering in the 21st
century
J. Lasenby, A.N. Lasenby and C.J.L. Doran
Phil. Trans. R. Soc. Lond. A 358, 21-39 (2000)
Quadratic
Lagrangians and topology in gauge theory gravity
A. Lewis, C. Doran and A.N. Lasenby
General Rel. Grav. 32(1), 161 (2000)
Microwave
Background Anisotropies and Nonlinear Structures I. Improved Theoretical
Models
A.N. Lasenby, C.J.L. Doran, M.P. Hobson, Y.Dabrowski and A.D. Challinor
Mon. Not. R. Astron. Soc. 302, 748--756 (1999).
Microwave
Background Anisotropies and Nonlinear Structures II. Numerical computations
Y.Dabrowski, M.P. Hobson, A.N. Lasenby and C.J.L. Doran
Mon. Not. R. Astron. Soc. 302, 757--770 (1999)
Geometric
algebra and the causal approach to multiparticle quantum mechanics
S.S. Somaroo, A.N. Lasenby and C.J.L. Doran
J. Math. Phys. 40(7), 3327-3340 (1999)
JMP
Multilinear
Representations of Rotation Groups within Geometric Algebra
M. A. J. Ashdown, S. S. Somaroo, S. F. Gull, C. J. L. Doran and A. N.
Lasenby
J. Math. Phys. 39(3), 1566-1588 (1998)
Effects
of spin-torsion in gauge theory gravity
C.J.L Doran, A.N. Lasenby, A.D. Challinor and S.F. Gull
J. Math. Phys. 39(6), 3303--3321 (1998)
Gravity,
gauge theories and geometric algebra
A. N. Lasenby, C. J. L. Doran and S. F. Gull
Phil. Trans. R. Soc. Lond. A 356, 487-582 (1998)
New
Geometric Methods for Computer Vision
J. Lasenby, W. J. Fitzgerald, C. J. L. Doran and A. N. Lasenby
Int. J. Comp. Vision 36(3), p. 191-213 (1998)
Massive,
non-ghost solutions for the Dirac field coupled self-consistently to gravity
A.D. Challinor, A.N. Lasenby, C.J.L. Doran and S.F. Gull
General Rel. Grav. 29, 1527 (1997)
Tunnelling
times of electrons
A. D. Challinor, A. N. Lasenby, S. S. Somaroo, C. J. L. Doran and S. F.
Gull
Phys. Lett. A, 227, 143-152 (1997)
The
physics of rotating cylindrical strings
C. J. L. Doran, A. N. Lasenby and S. F. Gull
Phys. Rev. D 54(10), 6021-6031 (1996)
A
relativistic, causal account of spin measurement
A. D. Challinor, A. N. Lasenby, S. F. Gull and C. J. L. Doran
Phys. Lett. A 218, 128-138 (1996)
Spacetime
Algebra and Electron Physics
Chris Doran, Anthony Lasenby, Stephen Gull, Shyamal Somaroo and Anthony
Challinor
Advances in Imaging and Electron Physics 95, 271-386
(1996)
Grassmann
Calculus, Pseudoclassical Mechanics and Geometric Algebra
A. N. Lasenby, C. J. L. Doran and S. F. Gull
J. Math. Phys. 34(8), 3683-3712 (1993)
Lie
Groups as Spin Groups
C. J. L. Doran, D. Hestenes, F. Sommen and N. van Acker
J. Math. Phys. 34(8), 3642-3669 (1993)
Imaginary
Numbers are not Real - the Geometric Algebra of Spacetime
S. F. Gull, A. N. Lasenby and C. J. L. Doran
Found. Phys. 23(9), 1175-1201 (1993)
States
and Operators in the Spacetime Algebra
C. J. L. Doran, A. N. Lasenby and S. F. Gull
Found. Phys. 23(9), 1239-1264 (1993)
A
Multivector Derivative Approach to Lagrangian Field Theory
A. N. Lasenby, C. J. L. Doran and S. F. Gull
Found. Phys. 23(10), 1295-1327 (1993)
Electron
Paths, Tunnelling and Diffraction in the Spacetime Algebra
S. F. Gull, A. N. Lasenby and C. J. L. Doran
Found. Phys. 23(10), 1329-1356 (1993)
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Conference Proceedings
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
A
Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a 6-D
Euclidean Vector Space
Timothy Havel and Chris Doran
Proc. SPIE, vol. 5436 (Quantum Information and Computation II, E Donkor,
A. R. Pirich & H. E. Brandt, eds.), pp. 93-106 (2004)
Applications
of Geometric Algebra in Electromagnetism, Quantum Mechanics and Gravity
A.N. Lasenby, C.J.L. Doran and E. Arcaute
In R. Ablamowicz, ed. Sixth International Conference on Clifford Algebras
and their Applications, Tennessee 2002, p. 467, Birkhauser (2003)
Geometric
Algebra, Dirac Wavefunctions and Black Holes
Anthony Lasenby and Chris Doran
In P.G. Bergmann and V. de Sabbata eds, Advances in the Interplay Between
Quantum and Gravity Physics, 251-283, Kluwer (2002).
Conformal
Geometry, Euclidean Space and Geometric Algebra
Chris Doran, Anthony Lasenby and Joan Lasenby
In J. Winkler ed Uncertainty in Geometric Computations, p.41 Kluwer
(2002).
Jet
Bundles and the Formal Theory of Partial Differential Equations
R.C.D. Baker and C.J.L. Doran
In C. Doran, L. Dorst and J. Lasenby eds. Applied Geometrical Algebras
in computer Science and Engineering AGACSE 2001, p. 133 Birkhauser (2002).
math.AP/0106090
Interaction
and Entanglement in the Multiparticle Spacetime Algebra
T.F. Havel and C.J.L. Doran
In C. Doran, L. Dorst and J. Lasenby eds. Applied Geometrical Algebras
in computer Science and Engineering AGACSE 2001, p. 227 Birkhauser (2002).
quant-ph/0106063
Analysis
of 1 and 2 Particle Quantum Systems using Geometric Algebra
R.F. Parker and C.J.L. Doran
In C. Doran, L. Dorst and J. Lasenby eds. Applied Geometrical Algebras
in computer Science and Engineering AGACSE 2001,p. 213 Birkhauser (2002).
quant-ph/0106055
Geometric
algebra in quantum information processing
T.F. Havel and C.J.L. Doran
In S.J. Lomonaco & H.E. Brandt, eds. Quantum Computation and Information,
Contemporary Mathematics 305, p. 81, AMS (2002).
quant-ph/0004031
Bayesian
inference and geometric algebra: an application to camera localization
C.J.L. Doran
In: E. Bayro and G. Sobczyk eds. Geometric algebra: a geometric approach
to computer vision, neural and quantum computing, robotics and engineering,
p. 172, Birkhauser (2000).
Electron
scattering in the spacetime algebra
A. Lewis, A.N. Lasenby and C.J.L. Doran.
R. Ablamowicz and B. Fauser eds., 5th International Conference on Applications
of Clifford Algebra, Ixtapa, Mexico 1999, 49-71 Birkhauser (2000).
Rotating
astrophysical systems and a gauge theory approach to gravity
A. N. Lasenby, C. J. L. Doran, Y. Dabrowski and A. D. Challinor
In N. Sanchez and A. Zichini, editors, Current Topics in Astrofundamental
Physics, Erice 1996, p. 380-403, World Scientific Publishing
Co (1997)
Geometric
algebra, spacetime physics and gravitation
S. F. Gull, A. N. Lasenby and C. J. L. Doran
In O. Lahav, E. Terlevich and R. J. Terlevich, editors, Gravitational
Dynamics, p. 171-180, Cambridge University Press (1996)
Lectures
in Geometric Algebra
A. N. Lasenby, C. J. L. Doran and S. F. Gull
In W. E. Baylis, editor, Clifford (Geometric) Algebras with Applications
to Physics, Mathematics and Engineering, BirkhДuser Boston (1996)
Astrophysical
and Cosmological Consequences of a Gauge Theory of Gravity
A. N. Lasenby, C. J. L. Doran and S. F. Gull
In N. Sanchez and A. Zichichi, eds. Advances in Astrofundamental Physics.
Erice 1994, p. 359-401, World Scientific Publishing Co. (1995)
Gravity
as a Gauge Theory in the Spacetime Algebra
C. J. L. Doran, A. N. Lasenby and S. F. Gull.
In F. Brackx and R. Delanghe, editors, Clifford Algebras and their
Applications in Mathematical Physics. Deinze 1993, p. 375-385, Kluwer
Academic, Dordrecht (1993)
Cosmological
Consequences of a Flat-Space Theory of Gravity
A. N. Lasenby, C. J. L. Doran and S. F. Gull
In F. Brackx and R. Delanghe, editors, Clifford Algebras and their
Applications in Mathematical Physics. Deinze 1993, p. 387-396, Kluwer
Academic, Dordrecht (1993)
Grassmann
Mechanics, Multivector Derivatives and Geometric Algebra
C. J. L. Doran, A. N. Lasenby and S. F. Gull
In Z. Oziewicz, A. Borowiec and B. Jancewicz, editors, Spinors, Twistors,
Clifford Algebras and Quantum Deformations, p. 215-226 Kluwer Academic,
Dordrecht (1993)
2-spinors,
Twistors and Supersymmetry in the Spacetime Algebra
A. N. Lasenby, C. J. L. Doran and S. F. Gull
In Z. Oziewicz, A. Borowiec and B. Jancewicz, editors, Spinors, Twistors,
Clifford Algebras and Quantum Deformations, p.233-245, Kluwer Academic,
Dordrecht (1993)
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