Daily Archives: October 2, 2007

A Fictitious Snuark Vacuum State

The calculations for the NNLO and higher corrections to the snuark mass interaction are difficult. I’ve already got some sort of sign error. Before I go on, I’m going to write a computer program to do the higher level calculations.

Of course it is possible, and even natural, to write a Java program to do snuark QFT calculations. One can implement the Pauli algebra projection operators for spin in the +/- x, y, and z directions, and multiply away. One computes the phases by writing the product of projection operators, for example, \rho_x\;\rho_y\;\rho_z as a complex constant k times the final and initial projection operators: \rho_x\;\rho_y\;\rho_z = k \rho_x\;\rho_z , or in Pauli matrix form:
XYZ to k XZ projection operator reduction

In the same manner, arbitrarily long products of projection operators can be reduced to a complex multiple of the initial and final projection operators. If there is a forbidden transition somewhere in that product, then the complex multiple will be zero. For the above product, k = \sqrt{0.5}\exp(i\pi/4) .
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