References

The reference list below is limited.  I will post the abstracts of the articles later and remove this list.  Articles in ArXiv on geometric algebra are now individually posted in this blog up to the 12 July 2009; they are not included in list.  I decided to do this instead of making webpages for each article, since I found that Google can find my posts after a few hours, but not my new pages even after a few months.  To find the references that you need, type the key words and/or author names on the search form at the upper right hand corner of this blog.  Seek and you shall find.

If you like me to post abstracts of your papers on Clifford (geometric) algebra in this blog, fill up the Comment Form below.  Or better, send me a link to your webpages containing your abstracts.  I shall post them the day after if I am not busy.  For conference announcements, go to the GA Net Updates blog by Eckhard Hitzer instead.

These are the unposted references:

Books

Rafal Ablamowicz and Bertfried Fauser, eds., Clifford Algebras and their Applications in Mathematical Physics (Birkhauser, Boston, 2000).

William E. Baylis, ed., Clifford (Geometric) Algebras with Applications to Physics, Mathematics, and Engineering (Birkhauser, Boston, 1996)

William E. Baylis, Electrodynamics: A Modern Geometric Approach (Birkhauser, Boston, 1999)

E. Folke Bolinder and Pertti Lounesto, eds., Clifford Numbers and Spinors by Marcel Riesz (Kluwer Academic, Dordrecht, 1993).

Ramon Gonzalez Calvet, Treatise of Plane Geometry through Geometric Algebra (R. G. Calvet, 2007).

J. S. R. Chisholm and A. K. Common, eds., Clifford Algebras and
Their Applications in Mathematical Physics (D. Reidel,
Dordrecht, 1986).

Chris Doran and Anthony Lasenby, Geometric Algebra for Physicists (Cambridge U.P., Cambridge,
U.K., 2003)

Leo Dorst, Chris Doran, and Joan Lasenby, eds., Applications of Geometric Algebra in Computer Science and Engineering (Birkhauser, Boston, 2002). 478 pages.

K. Gurlebeck and W. Sprossig, Quaternionic and Clifford Calculus for Physicists and Engineers (Wiley, Chichester, 1997).

D. Hestenes, New Foundations for Classical Mechanics (Reidel Dordrecht, 1990), 2nd ed., pp. 54–61.

David Hestenes, and Garret Sobcyk, Clifford Algebra to Geometric Calculus (Reidel, Dordrecht, 1984).

Bernard Jancewicz, Multivectors and Clifford Algebra in Electrodynamics (World Scientific, Singapore, 1988).

J. B. Kuipers, Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality (Princeton U.P., Princeton, NJ, 2002).

Pertti Lounesto, Clifford Algebras and Spinors (Cambridge U.P., Cambridge, UK, 2001).

Ian R. Porteous, Topological Geometry (Van Nostrand, London, 1969).

Ian R. Porteous, Clifford Algebras and the Classical Groups (Cambridge University Press, Cambridge, UK, 2000).

Clifford Analysis

W. E. Baylis, J. Huschilt, and Jiansui Wei, “Why i?” Am. J. Phys. 60, 788-797 (1992).

Jean Gallier, “Clifford algebras, Clifford groups, and a generalization of quaternions: the pin and spin groups,” in arXiv:0805.0311v1 [math.GM].

D. Hestenes, ‘‘Oersted Medal Lecture 2002: Reforming the mathematical language of physics,’’ Am. J. Phys. 71(2), 104–121 (2003).

Chris Pritchard, “Flaming swords and hermaphrodite monsters: Peter Guthrie Tait and the promotion of quaternions,” in Mathematical Gazette 82(494), 235–241 (1998).

Pertti Lounesto, “Marcel Riesz’s work on Clifford algebras,” in Clifford Numbers and Spinors by Marcel Riesz, ed. by E. Folke Bolinder and Pertti Lounesto (Kluwer Academic, Dordrecht, 1993), pp. 215–241.

Richard Baker and Chris Doran, “Jet bundles and the formal theory of partial differential equations,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 133-144.

Michael A. Baswell, Rafal Ablamowicz, and Joe N. Anderson, “Clifford algebra space singularities of inline planar platforms,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 407-422.

W. E. Baylis and S. Hadi, “Rotations in n dimensions as spherical vectors,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 79-90.

Stephen Blake, “Unification of Grassmann’s progressive and regressive products using the principle of duality,” in Applications of Geometric Algebra in Computer Science and Engineering (Birkhauser, Boston, 2002), pp. 3-34.

Timaeus Bouma, “From unoriented subspaces to blade operators,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 59-68.

Leo Dorst, “The inner products of geometric algebra,” in Applications of Geometric Algebra in Computer Science and Engineering (Birkhauser, Boston, 2002), pp. 3-34.

Seamus D. Garvey, Michael I. Friswell, and Uwe Prells, “The Role of Clifford algebra in structure-preserving transformations for second-order systems,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 351-360.

Neil Gordon, “Geometric and algebraic canonical forms,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 91-96.

Eckhard M. S. Hitzer, “Imaginary eigenvalues and complex eigenvectors explained by real geometry,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 145-156.

Cemal Koc and Songul Esin, “Annihilators of principal ideals in the Grassmann algebra,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 193-194.

Uwe Prells, Michael I. Friswell, and Seamus D. Garvey, “Compound matrices and Pfaffians: a representation of geometric algebra,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 109-118.

John Snygg, “Functions of Clifford numbers or square matrices,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 99-108.

Frank Sommen, “Analysis using abstract vector variables,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 119-128.

Computer Science and Engineering

Eduardo Bayro-Corrochano and Sandino Flores, “Color edge detection using rotors,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 333-340.

Eduardo Bayro-Corrochano, Pertti Lounesto, and Leo Reyes Lozano, “Applications of algebra of incidence in visually guided robotics,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 361-372.

Jeffrey A. Chard and Vadim Shapiro, “A multivector data structure for differential forms,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 129-132.

Michael Felsberg and Gerald Sommer, “The structure multivector,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 437-446.

John B. Fletcher, “Cliford numbers and their inverses calculated using the matrix representation,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 169-178.

John B. Fletcher, “Symbolic processing of Clifford numbers in C++,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 157-168.

Alyn Rockwood and Shoeb Binderwala, “A toy vector field based on geometric algebra,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 187-192.

Erwin Hocevar, “An algorithm to solve the inverse IFS-problem,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 459-468.

Jan J. Koenderink, “A generic framework for image geometry,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 319-332.

V. Labunets, E. Rundblad, and J. Astola, “Fast quantum Fourier-Heisenberg-Weyl transforms,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 425-436.

V. Labunets, E. Rundblad, and J. Astola, “Fast quantum n-D Fourier and Radon transforms,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 469-478.

V. Labunets, E. Rundblad, and J. Astola, “Is the brain a ‘Clifford Algebra quantum computer’?,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 285-296.

Hongbo Li, “Automated theorem proving in the homogenous model with Clifford bracket algebra,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 69-78.

W. Neddermeyer, M. Schnell, W. Winkler, and A. Lilienthal, “Stabilization of 3D pose estimation,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 385-394.

Christian B. U. Perwass and Gerald Sommer, “Numerical evaluation of versors with Clifford algebra,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 341-350.

Bodo Rosenhahn, Oliver Granert, and Gerald Sommer, “Monocular pose estimation of kinematic chains,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 373-384.

Hiniduma Udugama Gamage Sahan Sajeewa and Joan Lasenby, “Inferring dynamical information from 3D position data using geometric algebra,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 395-406.

Chemistry

John P. Fletcher, “The Application of Clifford algebra to calculations of multicomponent chemical composition,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 449-458.

Patrick Girard, “Quaternions, Clifford algebra and symmetry groups,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 307-316.

David Hestenes, “Point groups and space groups in geometric algebra,” in Applications of Geometric Algebra in Computer Science and Engineering (Birkhauser, Boston, 2002), pp. 3-34.

Janne Pesonen, “Exact kinetic energy operators for polyatomic molecules,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 261-270.

Electrodynamics

W. E. Baylis, J. Bonenfant, J. Derbyshire, and J. Huschilt, ‘‘Light polarization: A geometric algebra approach,’’ Am. J. Phys. 61, 534–544 (1993).

Bernard Jancewicz, “Trivector Fourier transformation and electromagnetic field,” J. Math. Phys. 31, 1847-1852 (1990).

Bernard Jancewicz, “A Hilbert space for the classical electromagnetic field,” Foundations of Physics 23(11), 1405-1421 (1993).

Terje Vold, “Introduction to geometric algebra and its application to electrodynamics,” Am. J. Phys. 61, 505-513.

Quirino M. Sugon Jr. and Daniel J. McNamara, “A Hestenes spacetime algebra approach to light polarization,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 297-306.

Geometric Optics

Mike Derome, “Laws of reflection from two or more plane mirrors in succession,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 249-260.

Mechanics

Terje Vold, ‘‘An introduction to geometric algebra with application in rigid body mechanics,’’ Am. J. Phys. 61, 491–504 (1993).

David Hestenes and Ernest D. Fasse, “Homogenous rigid body mechanics with elastic coupling,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 197-212.

Quantum Theory

David Hestenes, “Vectors, spinors and complex numbers in classical and quantum physics,” Am J. Phys. 39, 1013-1027 (1971).

Timothy F. Havel and Chris J. L. Doran, “Interaction and entanglement in the multiparticle spacetime algebra,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 227-248.

T. Schulte-Herbruggen, K. Huper, U. Helmke, and S. J. Glaser, “Geometry of quantum computing by Hamiltonian dynamics of spin ensembles,” in Applications of Geometric Algebra in Computer Science and Engineering, ed. by Leo Dorst, Chris Doran, and Joan Lasenby (Birkhauser, Boston, 2002), pp. 271-284.

Relativity Theory

B. K. Datta and V. de Sabbata, “Hestenes’ geometric algebra in real spinor fields,” in Spin in Gravity: Is it Possible to give an experimental basis to torsion?, International School of Cosmology and Gravitation Course, Erice, Italy, 13-20 May 2007 (World Scientific, Singapore, 1997), pp. 33-50.