I’ve just submitted a paper, Density Matrices and the Weak Quantum Numbers to Foundations of Physics. There are things about the paper that I didn’t include, things that I didn’t think were appropriate to a journal submission and I thought I’d talk about them here, and explain what the paper is talking about to a more general (but still math/physics) audience.
The paper is on the subject of the weak quantum numbers of the left and right handed elementary fermions and anti-fermions. Ignoring color and generation, there are 16 of these quantum objects. I provide a method of defining these quantum numbers by an idempotency equation, that is, by solving an equation of the form . Since pure density matrices satisfy this equation, the calculation is a density matrix calculation based on the permutation group on 3 elements.
The usual method of elementary particles is to assume that a symmetry relates the quantum states. In this calculation, the quantum states themselves are assumed to be composed of group elements of the symmtry. This can be done in density matrix formalism because density matrices can operate on themselves. Also of interest are what happens when different density matrices operate on each other. Particularly when the density matrices are chosen from the basis states of a complete set of mutually unbiased bases. But that’s another paper (mostly written).