The Living Thing / Notebooks :

Differential geometry, geometric algebra etc

TBD. A pragmatic guide to manifold wrangling, whatever your formalism.

Key words: Clifford algebra, differential forms…

See also information geometry.

TBD.

Clifford Algebra formalism

Hestenes’ school.

Handy texts:

Differential forms formalism

Refs

Amar01
Amari, S. (2001) Information geometry on hierarchy of probability distributions. IEEE Transactions on Information Theory, 47, 1701–1711. DOI.
Bach03
Bachman, D. (2003) A Geometric Approach to Differential Forms.
BrRi95
Brody, D., & Rivier, N. (1995) Geometrical aspects of statistical mechanics. Phys. Rev. E, 51(2), 1006–1011. DOI.
Chis12
Chisolm, E. (2012) Geometric Algebra. arXiv:1205.5935 [Math-Ph].
DoLa15
Doran, C., & Lasenby, A. (2015) Physical applications of geometric algebra.
DoLa03
Doran, C., & Lasenby, A. N.(2003) Geometric algebra for physicists. . Cambridge ; New York: Cambridge University Press
DoFM10
Dorst, L., Fontijne, D., & Mann, S. (2010) Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry. . Morgan Kaufmann
Flan89
Flanders, H. (1989) Differential Forms with Applications to the Physical Sciences. . Dover Publications
Hest88
Hestenes, D. (1988) Universal geometric algebra.
Hest91
Hestenes, D. (1991) The design of linear algebra and geometry. Acta Applicandae Mathematica, 23(1), 65–93. DOI.
Hest03
Hestenes, D. (2003) Spacetime physics with geometric algebra. American Journal of Physics, 71(7), 691–714. DOI.
HeSo84
Hestenes, D., & Sobczyk, G. (1984) Clifford Algebra to Geometric Calculus a Unified Language for Mathematics and Physics. . Dordrecht: Springer Netherlands
Hest01
Hestenes, P. D.(2001) Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry. In D. E. B. Corrochano & P. G. Sobczyk (Eds.), Geometric Algebra with Applications in Science and Engineering (pp. 3–17). Birkhäuser Boston DOI.
LaLD00
Lasenby, J., Lasenby, A. N., & Doran, C. J. L.(2000) A unified mathematical language for physics and engineering in the 21st century. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 358(1765), 21–39. DOI.
Laur87
Lauritzen, S. L.(1987) Statistical manifolds. In Differential geometry in statistical inference (p. 164). JSTOR
LPRS10
Leibon, G., Pauls, S., Rockmore, D., & Savell, R. (2010) Statistical Learning for Complex Systems an Example-driven Introduction.
Macd16
Macdonald, A. (2016) A Survey of Geometric Algebra and Geometric Calculus. Advances in Applied Clifford Algebras, 1–39. DOI.
Moor93
Moore, C. (1993) Braids in classical dynamics. Physical Review Letters, 70(24), 3675–3679.
WaAr96
Warnick, K. F., & Arnold, D. V.(1996) Electromagnetic Green functions using differential forms. Journal of Electromagnetic Waves and Applications, 10(3), 427–438. DOI.
WaAS96
Warnick, K. F., Arnold, D. V., & Selfridge, R. H.(1996) Differential forms in electromagnetic field theory. In Antennas and Propagation Society International Symposium, 1996. AP-S. Digest (Vol. 2, pp. 1474–1477 vol.2). DOI.
WaSA95
Warnick, K. F., Selfridge, R. H., & Arnold, D. V.(1995) Electromagnetic boundary conditions and differential forms. IEE Proceedings-Microwaves, Antennas and Propagation, 142(4), 326–332. DOI.
WaSA96
Warnick, K. F., Selfridge, R. H., & Arnold, D. V.(1996) Electromagnetics made easy: differential forms as a teaching tool. In 2013 IEEE Frontiers in Education Conference (FIE) (Vol. 3, pp. 1508–1512). IEEE
WaSA97
Warnick, K. F., Selfridge, R. H., & Arnold, D. V.(1997) Teaching electromagnetic field theory using differential forms. IEEE Transactions on Education, 40(1), 53–68. DOI.