Truly pointed out - The mathematical uniqueness of the Moyal bracket (as the only one-parameter Lie-algebraic deformation of the Poisson bracket) implies that the commutator structure of quantum mechanics is the unique way to achieve a strict lower bound on entropy.
It IS related to geometric algebra cuz you use Lie algebra for describing smooth movements and rotations—like spinning a ball (“infinitesimal” steps or actions that build complex movements), and then you expand it to form patterns and symmetries commutatively. It's a great tool for quantum mechanics :)
Truly pointed out - The mathematical uniqueness of the Moyal bracket (as the only one-parameter Lie-algebraic deformation of the Poisson bracket) implies that the commutator structure of quantum mechanics is the unique way to achieve a strict lower bound on entropy.
I've heard about those because of some projected geometric algebra thing but I dont understand it
It IS related to geometric algebra cuz you use Lie algebra for describing smooth movements and rotations—like spinning a ball (“infinitesimal” steps or actions that build complex movements), and then you expand it to form patterns and symmetries commutatively. It's a great tool for quantum mechanics :)