Re: Attraction vs repulsion - why does it depend on spin?

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Date: 28 Feb 2005 15:22:04 -0800

What the "French" experiment shows is that if you treat the earth's
gravity field with Schrodinger's equation, you get discrete energy
states. The simple calculation was actually done years back in,
"Problems And Solutions In Quantum Chemistry And Physics," Charles S.
Johnson Jr. and Lee G. Pedersen, Dover, 1986, ISBN: 0-486-65236-X
Problem number 4.14 page118-119.

Papers that directly treat the question of how spin affects attraction
or repulsion between like "charges" (be these like electrical charges
for electric charge, or other more general charges) are:

Steven Weinberg, "Feynman Rules for any spin," Physical Review, Vol.
133, No. 5B, 9 March 1964

Huang Shi-Zhong et. al, "Projection Operator and Propagator for an
Arbitrary Integral Spin," Chin. Phys. Lett. Vol. 19, No. 12, 2002, p.
1767

Huang Shi-Zhong et. al., "Feynman Propagator for an arbitrary
half-integral spin," Chinese Physics, Vol. 12, No. 7, July 2003

The Wigner paper, one of the most cited papers in physics, is,

E. Wigner, "On Unitary Representations of the Inhomogeneous Lorentz
Group," The Annals of Mathematics, 2nd Ser., Vol 40, No. 1 (Jan. 1939),
p. 149-204.

This paper develops a lot of the mathematics required to do quantum
field theor with respect to group theory.

If you understand the quantum mechanics of angular momentum and
addition of angular momentum in terms of Jx, Jy, Jz, J^2, J+ and J-
operators, their eigenvalues and the matrix elements they generate,
then H. F. Jones, "Groups, Representations and Physics," 2nd. ed.,
chapter 8 will allow you to calculate particle spectra such as
3X3X3=10+8+8+1 for baryons (3 quarks) and 3X3*=6+3 for mesons (1 quark,
1 anti quark). J. J. Sakurai, "Modern Quantum Mechanics" does a great
job of explaining the use of the Young Tableau to simply calculating
particle spectra.

Again, Zee, "Quantum Field Theory in a nutshell," somewhere in the
first part of the book, shows what a particle of spin to acts and
smells like a graviton.

>>From a classical point of view, one may expand an electromagnetic field
in terms of multipoles (spherical harmonics). The spherical harmonics
have an l and m index which, when solving for the hydrogen atom,
represent the orbital angular momentum eigenvalues, and the z-axis
(arbitrarily chosen axis) eigenvalues. A positve and and negative
charge separated by a finite distance define a dipole, hence, with this
kind of classical argument we can say a photon (creator of
electromagnetic fields) has spin 1. That is l=1. One, however, cannot
make a gravity dipole as we don't seem to have antigravitating mass.
The next best thing we can do is build a quadrupole, hence l=2, hence
spin 2 particle. To be honest, I don't really like these "artificial"
classical arguments, but they may help to clear give one a picture.

Recall the hydrogen atom solved by Schrodinger's equation. It is
desribed by 3 quantum numbers: n = energy level, l = orbital angular
momentum and mz=-l, -l+1,...,0,...,l-1,l. The electron spin quantum
number, if there are no external magentic fields, and if we ignore the
interaction of the electron spin with the proton spin, can be ignored
as negligible. Whenever such a simple hydrogen atom radiates, changing
n, l and mz, the photons must, by energy conservation, be carrying
these quantum numbers.

Cheers,

AA

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