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

From: George Jones (george_llew_jones_at_yahoo.com)
Date: 03/01/05 

Date: Tue, 01 Mar 2005 08:18:55 -0500

francoisbelfort@yahoo.fr wrote:
> akalaniz@hotmail.com wrote:
>
>>An outline as to why spin is involved in determining whether a force
>>between two like charges is attractive or repulsive may be found in
>>part I of Zee's, "Quantum Field Theory in a nutshell." The full
>>reason lies in the abstract algebra (group theory) of special relativity
>>and SU(N) groups. Wigner published a paper on this in the 1930s.
>>
>>AA
>
> Hm, ok, but is there a simple way to understand it? This
> text is probably out of my reach.
> (Spin 2 is already a classical property of gravity (waves) -
> independently whether gravitons exist or not.
> And spin 2 forces are always attractive, whereas spin 1 mediated forces
> can be either attractive or repulsive.)
>
> And is there a reference for the Wigner paper? I'd like to read it ...

The reference is

E.P. Wigner, On the representations of the inhomogeneous Lorentz group,
Ann. of Math. v40, 149-204 (1939).

Also relevant is

E. Wigner and V. Bargmann, group theoretical discussions of relativistic
wave equations, Proc. Nat. Acad. Sci. V34, 211-223, (1948).

Wigner's 1939 paper is *much* more difficult to read than Zee's text.
This classic paper, which treats the fundamental heart of the marriage
of quantum theory and special relativity, is one of the few examples of
a post 1900 paper that simultaneously made fundamental advances in
physics and mathematics by the standards of each.

However, for reasons I will give in a reply to AA, the paper has almost
*nothing* to say about the SU(N) groups.

I encourage you to get hold of a copy of Zee's book. The whole text is
informal, with part I being particularly informal. As AA says, Zee
gives the answer to your question. Chapter I.5, which starts on page 30,
is titled Coulomb and Newton: Repulsion and Attraction.

Like Franz, I don't see how spin 2 falls out classically. When
general relativity is linearized, a relativistic wave equation can be
derived. This wave equation is for spin 2, but the reasons come from
quantum theory.

Regards,
George
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