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Clifford or geometric algebra generalizes this to spinors in any dimension and signature, so you also get the dirac equation for free in a sense
by nimish 5y ago
Clifford or geometric algebra generalizes this to spinors in any dimension and signature, so you also get the dirac equation for free in a sense
- BlueTemplar 5y agoYeah, quaternions didn't seem that exceptional, "just" the generalization to rotations in 3D, but Geometric Algebra did get me excited because I finally managed to understand what was the whole deal with those weird "pseudo-vectors"... https://www.av8n.com/physics/clifford-intro.htm https://www.av8n.com/physics/clifford-intro.htm
- andi999 5y agoYour link does not explain rotation with Clifford algebra (except 90 degree rotations)
- BlueTemplar 5y agoYeah there's a whole dedicated webpage about that : https://www.av8n.com/physics/rotations.htm https://www.av8n.com/physics/rotations.htm > In this document, we discuss rotations, including simple rotations in the plane but also including compound rotations around multiple axes in three or more dimensions. We briefly survey four ways of pictorially representing rotations: two vectors in the plane of rotation, triad before and after rotation, axis plus amount of rotation, and yaw/pitch/roll. These can (respectively) be formalized in terms of (respectively) Clifford algebra i.e. quaternions, matrices, Rodrigues vectors, and Euler angles.