Bound States as Symmetry Operators and E8

Previously, we saw that density operators generate symmetries in the set of quantum states and that these new symmetries gave non Hermitian quantum states. We then saw that bound states of Feynman diagrams can be represented by matrices of these non Hermitian quantum states. In this post, we use these matrices of non Hermitian quantum [...]

Bound States as Density Matrices

Review: Previously, we showed that non Hermitian density matrices arise naturally as the result of using density matrices to define symmetry operations on density matrices, and that these sorts of things might be used in defining Feynman diagrams modeling bound states. We begin with a proton modeled as a set of three valence quarks held [...]

Non Hermitian Density Matrices

Recently Garrett Lisi’s used a broken E8 symmetry to classify the known elementary particles. I believe that E8 arises naturally from composite particles. The outline of the argument (as covered in the first post) amounts to noticing that E8 is unique among the simple Lie algebras in that “in the context of linear algebra, E8 [...]

Quantum States as Symmetry Operators

The first step in seeing how a broken E8 can arise by treating composite particles as if they were elementary consists in understanding how it is that a quantum state can be interpreted as a symmetry operator. That is the subject of this post. The remaining steps are outlined in the previous post.
We begin with [...]

Broken E8 as a Result of Composite Particles I

Since I think that the standard model particles are composite, it’s natural, with Garrett Lisi’s use of E8, to wonder if E8 can arise naturally as a result of composite particles. I think it can. I will use the fact that as Baez puts it, “This means that in the context of linear algebra, E8 [...]