G(x,x”) = \int G(x,x’) G(x’,x”) dx’

See the multiplication in the above? Physically, a Hermitian PI is an example of a Stern-Gerlach filter. The product of two of them means putting the output of one filter into the input of another. The theorem says that any two Hermitian PIs can be written as a NHPI with a real loss of amplitude.

]]>The difference is sort of like how complex numbers are a generalization of real numbers, and one can write a complex number from two real numbers (in a number of ways, the one being sort of similar to this is r and theta). The complex numbers can solve problems that the real numbers cannot.

I signed up for sci.physics.foundations. It’s moderated, but allows weirder posts than usual. Too bad it’s in text format.

There are some interesting articles there by Jay Yablon. One suggests that electrons, muons and taus are composite based on magnetic moments.

One other thing. I’ve got the Java program to convert 3×3 matrices of products of NHPIs into 3×3 matrices of complex numbers. The test is like the diagram chasing you category people like so much. Take a 3×3 matrix of Pauli NHPIs, convert it to complex, square it, and compare with the same 3×3 Pauli matrix, squared, and then converted.

The next task is to write the reverse conversion, to take a complex matrix into a 3×3 matrix of NHPIs. Since the PIs among the complex matrices are known, this gives an exact solution for the NHPIs. That code is written but it was late last night and I haven’t got it to work yet. Probably tonight.

]]>Splitting idempotents eh? Well consider writing any operator as the sum of a negative part and a positive part.

Hmmm, like when we were learning about spherical harmonics, the derivation in Sakurai involved splitting up an operator into 2 parts.

I know that any Unitary operator can be expressed as a linear transformation on a Hermitian operator E.G. U= H + i(dependent variable like time or position) And U naturally has an exponetial representation.

Hmm so what a Hermitian operator generates a non Hermitian operator that can be split into two parts. This is one answer to the question. Let us find some others…

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