I’m busily working on writing the CKM matrix in Kea’s form, that is, as a unitary matrix that is the sum of 1-circulant and 2-circulant matrices. With the MNS matrix this was easier because I could begin with a unitary matrix, but the CKM matrix is usually given in absolute value form.
Looking through the literature, [...]
Entries from July 2008
July 30, 2008
Unitarity and the CKM Matrix
July 24, 2008
Pop quiz! Spin Powers, and latest MNS news
I’ve been working on a derivation of the tribimaximal MNS matrix from first principles. It looks like it will require an assumption that the underlying particles follow a set of mutually unbiased bases (MUB). The calculation involves spin products. These are messy to compute unless you know some tricks I’ve discussed here previously.
So, [...]
July 14, 2008
Book Review: My One Contribution to Chess, F. V. Morley
The Crossroads chess club provides me with the entertainment of watching chess games, along with the discussion that is natural to accompany such. Only rarely does my excessive kibbitzing force me to accept a challenge to play; though I have been practicing with such books as 1001 Brilliant Ways to Checkmate, my ability is somewhat [...]
July 13, 2008
Electroweak unification, Quarks
To recap the previous post we began by combining the SU(2) spin-1/2 and U(1) operators into 2×2 matrices. We then showed that the leptons were solutions of the idempotency equation UU = U for 2×2 matrices subject to the additional requirement that the solutions be eigenstates of electric charge Q. For pure density matrix formalism, [...]
July 4, 2008
Electroweak Unification, Leptons
Quarks will require 1-circulant and 2-circulant matrices. Before adding that complication, let’s unify the lepton quantum numbers. Two quantum numbers (other than generation) distinguish quarks and leptons, weak hypercharge and weak isospin . Weak hypercharge is a U(1) quantum number; it has only one generator and therefore is commutative. Weak isospin arrives in two [...]
