Entries from September 2007

September 22, 2007

Infrared Correction to Mass I

Earlier we postulated the snuark mass interaction for a transition from a left to a right handed state as a simple iq vertex stuck between two propagators:

We postulated that the mass interaction that converts a left handed lepton to a right handed lepton involved three of these transitions happening simultaneously. We put the left handed [...]

September 20, 2007

Primitive Idempotents and Generations

In the previous post, we looked at long term bound snuark states, came up with three coupled quadratic equations in complex numbers I, J, and K:

noted that these equations are equivalent to a matrix idempotency equation:

wrote down the eight solutions:

and promised to interpret them in the next (this) post. Okay.

September 19, 2007

Long Lived Snuark Bound States

In the previous post we showed how we can take the left to right snuark mass interaction, and combine it with the right to left interaction, to make a left to right to left interaction, which we will somewhat abusively call a “LRL propagator”. The reason for calling it a propagator is because we are [...]

September 13, 2007

The Snuark Mass Interaction

In the standard model, the proton is made up of three quarks. The individual quarks are spin-1/2 particles. As elements of a QFT, the quarks are represented by propagators that satisfy the Dirac equation. What’s a bit odd is that the proton is also a spin-1/2 particle and is also represented by that same Dirac [...]

September 10, 2007

The Snuark Algebra as a QFT

The snuark algebra is simply a finite subset of the Pauli algebra, the subset generated by spin in the +x, +y, and +z directions. If we were to do our calculations by the usual methods of the Pauli algebra, we would choose an orientation, typically +z, and define the +x and +y states in terms [...]

September 3, 2007

The Algebra of Orthogonal Spin-1/2 States

Everybody knows that the quantum states of spin-1/2 particles come in two and only two independent spin orientations, for example spin +z and spin -z (up and down). My snuark theory uses spin-1/2 calculations to compute the Koide mass formulas, so it is a little inconvenient that snuarks need to come in six independent quantum [...]