The Net Advance of Physics:
GEOMETRIC and CLIFFORD ALGEBRA

GEOMETRIC & CLIFFORD ALGEBRA:

• General: Introductory: Gull et al. 93/02; Rodriguez 97/09;
  • Geometric Algebra of One and Many Multivector Variables by Janne Pesonen [University of Helsinki, 2007] About 200pp.; only first half of text available.
• General: Gull et al. 93/02; Doran (thesis) 94;
  • Applied Geometric Algebra by Lászlo Tiszá [Spring 1976] Complete lecture notes for a course in (middle 20th century style, non-Clifford) geometric algebra by one of MIT's most distinguished natural philosophers. (MIT OpenCourseWare)
  • Maths for (Games) Programmers by Ian C. G. Bell [begun 1998] The name of the site is misleading, and the headache-inducing wallpaper is unfortunate, but there are few geometric-algebra resources online which can rival this one. Topics include multivector calculus, multivector general-relativity, Hestenes's form of the Dirac equation, etc.
  • Geometric Algebra of One and Many Multivector Variables by Janne Pesonen [University of Helsinki, 2007] About 200pp.; only first half of text available.

  • Geometric Algebra by E. Artin [New York: Interscience, 1957] Classic text of the mid-Twentieth Century school.
  • Geometric Algebra for Physicists by Chris Doran and Anthony Lasenby [Cambridge University Press, 2003]. A complete textbook.

  • Relativistic Physics as Application of Geometric Algebra by Eckhard Hitzer [2005/01] This is a viXra paper, but the material is all standard and very well presented.
  • Spin and Clifford algebras, an introduction by Marc Lachieze-Rey [2010/07]
  • Geometric Algebra: A natural representation of three-space by James M. Chappell et al. [2011/01]
  • Clifford Algebras and Spinors by Ivan Todorov [Bulgarian Journal of Physics 38, 3 (2011)]
  • Geometric Algebra by Eric Chisolm [2012/05]
  • Introduction to Clifford's Geometric Algebra by Eckhard Hitzer [Journal of the Society of Instrument and Control Engineers 51, 338 (2012)]
  • Applications of Clifford's Geometric Algebra by Eckhard Hitzer et al. [Advances in Applied Clifford Algebras 23, 377 (2013)]
  • Introducing Geometric Algebra to Geometric Computing Software Developers by Ahmad Hosny Eid [2017/05]
  • From Vectors to Geometric Algebra by Sergio Ramos Ramirez et al. [2018/02]

• Types: CLIFFORD ALGEBRAS; GRASSMANN ALGEBRAS; QUATERNIONS; SCREWS; SPINORS; TWISTORS;

• Type: L-MATRICES:
  • On generalized Clifford algebras and their physical applications by R. Jaganathan [2010/05]

• Aspects: BIVECTORS:
  • Teaching rotational physics with bivectors by S. Jensen and J. Poling [2022/07]

• Aspects: CLIFFORD ANALYSIS & MULTIVECTOR CALCULUS: Ryan 2003/03;
  • Multivector Differential Calculus by Eckhard Hitzer [Advances in Applied Clifford Algebras 12, 135 (2002)]

• Re: ANGULAR MOMENTUM:
  • Teaching rotational physics with bivectors by S. Jensen and J. Poling [2022/07]

• Re: CONFORMALLY-FLAT MANIFOLDS: Ryan 2003/03;

• Re: FIELD THEORY: CLASSICAL: Echeverría-Enríquez et al. 2001/05;

• Re: FOURIER ANALYSIS: Ryan 2003/03;

• Re: HAMILTONIAN THEORY: Echeverría-Enríquez et al. 2001/05;

• Re: HARMONIC ANALYSIS: Ryan 2003/03;

• Re: LAGRANGIAN THEORY: Echeverría-Enríquez et al. 2001/05;

• Re: NEURAL NETS:
  • Introduction to Clifford's Geometric Algebra by Eckhard Hitzer [Journal of the Society of Instrument and Control Engineers 51, 338 (2012)]

• Re: ROTATION:
  • Teaching rotational physics with bivectors by S. Jensen and J. Poling [2022/07]
  • Rotations in classical mechanics using geometric algebra by S. D. Brechet [2022/10]

THE NET ADVANCE OF PHYSICS