Yang Mills Theory

When studying quantum mechanics, the Pauli matrices and the matrices of larger particles in their quantum number basis are represented in a complex Hilbert space. Extending these matrices is the heart of Yang Mills theory. Here, we expand the idea of representing the quantum spins, or any quantum number, to an n dimensional matrix. Yang Mills theory develops the Young Tableaux formalism, a way of geometrically interpreting the basis states of Pauli and Gell-Mann (the case of quarks). Quaternions, penternions, and n-ternions are these Yang Mills states, matrices, that develop in the scattering picture of quantum mechanics, where the amplituhedron represents the string geodesic landscape of multidimensional particles scattering (or interacting elastically and inelastically) in a fundamental geometry. The extension of the Yang Mills states to the amplituhedron can build a polytope in Hilbert space that changes the deterministic fate of particles into the shape of a fundamental Platonic-like solid.