Pauli Algebra
This is a website we're I'm collecting tools that have to do with
calculations made in the Pauli algebra using the principles of Julian
Schwinger's Measurement Algebra.
The following Java Applet uses Schwinger's "fictitious vacuum" to
compute products of Pauli projection operators. For a discription of
how this works, see my blog entries part 1, and part 2.
In short, you press buttons to enable a given projection operator. The projection operators (which are also density matrices
that represent quantum states) are labeled according to the direction
that they select spin, either the + or - x-axis, y-axis and z-axis. The
result of the calculation is the complex amplitude that is produced by
the sequence of projection operators. This is the amplitude that must
be assigned to the product of the final and initial projection
operators in order to make them equivalent to the given product of
projection operators.
By left clicking on buttons, you turn that projection operator on and
cause a calculation. If two consecutive projection operators are
incompatible measurements (i.e. spin up and spin down), the resulting
amplitude will be zero. If all the intermediate states are the same,
the complex amplitude will be unity. Since the answer is given as the
complex multiple that must be applied to the product of the initial and
final projection operators, these two oeprators have to be compatible.
To avoid a division by zero, the program will give these sorts of
calculations a result of zero.
I've set up the initial conditions to do the following computation:
I'll be upgrading this tool so that instead of simple products of
projection operators, it will do sums over classes of products of
projection operators. This is the basis of calculations in the Snuark QFT.
Hopefully, these calculations will give a method of deriving the mass
ratios of the leptons, in particular, the angle 0.22222204717 that
appears in Koide's equations.
Carl Brannen