Authors: C. A. Brannen
We present a new decomposition of unitary matrices particularly useful for mixing matrices. The decomposition separates the complex phase information from the mixing angle information of the matrices and leads to a new type of parameterization. We show that the mixing angle part of U(n) is equivalent to U(n-1). We give closed form parameterizations for 3x3 unitary mixing matrices (such as the CKM and MNS matrices) that treat the mixing angles equally. We show the relationship between Berry-Pancharatnam or quantum phase and the Jarlskog invariant Jcp that gives the CP-violation in the standard model. We established the likely existence of the new decomposition by computer simulation in 2008. Philip Gibbs proved the n=3 case in 2009 and in 2011, Samuel Lisi proved the general case using Floer theory in symplectic geometry. We give an accessible version of Lisi's proof.
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[v1] 2015-11-10 16:59:41
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