Geometric Algebra

Currently Playing: Classical and quantum physics | Geometric algebra episode 16

#geometricalgebra #pauli #dirac #spacetime #electromagnetism #mechanics It's time to look at a few concrete applications of geometric algebra in physics. We look at mechanics, where we unify linear and rotational motion. In vector calculus, we combine the divergence and curl into a single object, which helps us simplify the Maxwell equations. Then, in quantum physics, we discover that the Pauli and Dirac matrices are just representations of the familiar basis vectors. After this rapid-fire introduction, you may feel the need to explore further. Here are some really good resources: [SDK 1] https://www.youtube.com/watch?v=LQyKb0Flm3w Steven De Keninck explains the unification of forces and torques in classical mechanics. You can also download the PDF at https://bivector.net/PGAdyn.pdf. [MOM 1] https://www.youtube.com/watch?v=BcJGgG4HmwE Mathoma shows how to easily add 2 bivectors. He then shows how you can use these formulas to add torques together. [SUDGY 1] https://www.youtube.com/watch?v=60z_hpEAtD8 Gives a short but good introduction to what the Maxwell equations look like in GA. [AMD 1] http://www.faculty.luther.edu/~macdonal/GA&GC.pdf In chapter 3 of this free PDF, Alan MacDonald explains applications of geometric algebra in physics. [GLD 1] https://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/ImagNumbersArentReal.pdf Yet another very good introduction to geometric algebra. The applications in physics in the later chapters are more difficult for beginners like myself, but still very intriguing due to the many simplifications they manage to make to traditional formulas. You can support us on Patreon, where you can get access to exclusive content. Unfortunately, we won't be publishing any new videos after Geometric Algebra, at least not in the near future. Your support is still more than welcome of course: https://www.patreon.com/user?u=86649007 0:00 Introduction 0:27 Classical mechanics 2:32 Vector calculus: Gradient, divergence, and curl 5:19 Maxwell & electromagnetism 7:06 Pauli spin matrices 10:00 Dirac matrices 14:20 Please consider supporting our channel. We need your help! This video is published under a CC Attribution license ( https://creativecommons.org/licenses/by/4.0/ )