Re: Query about intrinsic verus orbital angular momentum

On Apr 14, 9:40 pm, "Jay R. Yablon" <jyab...@xxxxxxxxxxxx> wrote:

Finally, somebody has answered my question directly. Let me rephrase
what I think you mean:

We generate a rotation through angle psi about the z-axis by acting on a
wavefunction phi via with the z-axis rotation generator m, according to:

exp[i psi m] phi.

Because psi has a period of 2 pi, the eigenvalues of m must be an
integer, not a half integer. Am I correct so far?

If so, then my next question is this: Go to section 41.5 of Misner,
Wheeler, Thorne, where they discuss orientation / entanglement. There,
a rotation through 4pi is needed to restore not only orientation, but
the entanglement version. So, if psi needs a period of 4pi rather than
2pi to restore the entanglement relationship with the surrounding
environment, then the Eigenvalues of m can be half integers, and can be
generated -- not by the "rotation group" -- but by what one might call
the "entanglement / rotation" group. This would make it possible, I
believe, to create half-integer spin as well, from an rxp operator, with
the understanding that entanglement counts. This would appear to pave
the way to place the fundamental representation SO(1,3) of the Lorentz
group, which uses the SU(2) generators, onto an rxp operator footing as
well.

Your further thoughts.

Thanks,

Hi Jay,

A free Dirac electron has a phase which is equal throughout
its rest frame, so there is no such varying phase around the
wave-function.

Now, the effect which I describe in the first chapter in my
book is straightly from Sakurai's treatment of the Dirac
equation in his book: Advanced QM, chapter 3.5 "Gordon
decomposition"

http://physics-quest.org/Book_Chapter_EM_basic.pdf
section 1.9

For the analogy with magnetized media, Sakurai refers
to Jackson. The referred section has become section 5.8
in my 1999 copy, equation 5.79.


Regards, Hans

.

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