>>11733506No problem friend.
>General relativity and quantum mechanics I've already mentioned Szekeres' book so I will focus on initial work. The work of Lasenby and Doran presents a powerful abstraction use geometric algebras which not only has a more general formalism, but is also a more intuitive derivation of the Riemann, Ricci and Einstein tensors
http://www.mrao.cam.ac.uk/~clifford/publications/ps/anl_erice_2001.pdfIn this paper they present some useful applications in black hole scattering and some basic work on QM applications, most building on previous work, see for example this attempt:
S. Somaroo, D.G. Cory, and T.F. Havel. Expressing the operations of quantum
computing in multiparticle geometric algebra. Phys. Lett. A, 240:1–7, 1998.
The connected research group at Cambrigde is also continuing this work on computational clifford algebras, this library is open source:
https://github.com/pygae/clifford>Differential geometry, computational topology, and graphics processingSee the work done by Caltech and CMU groups that cite the 2003 thesis by Hirani (
https://thesis.library.caltech.edu/1885/3/thesis_hirani.pdf, many researchers have adopted this work. For example, many subsequent publications cite this work (currently over 450), see for example the applied side where many complex operators usually done by tensors are replaced with a more general discrete differential geometry formulation,
Desbrun M., Kanso E., Tong Y. (2008) Discrete Differential Forms for Computational Modeling. In: Bobenko A.I., Sullivan J.M., Schröder P., Ziegler G.M. (eds) Discrete Differential Geometry. Oberwolfach Seminars, vol 38. Birkhäuser Basel
See also for example the work done by CMU robotics group and the university of Göttingen.
https://www.ams.org/publications/journals/notices/201710/rnoti-p1153.pdf[cont.]
