🚀 go-pugleaf

In article <12950067@hpspdla.spd.HP.COM> ric@hpspdla.spd.HP.COM (Ric Peregrino) writes:

> How does masslessness lead to no spin 0 photons? If this is too deep,
> then a reference would suffice.

There are two answers, one of which is easy, but the other of which is
deep, and more interesting.

Answer one: naively, a photon would have three spin states.  When you
express this in terms of quantum fields (i.e., the electromagnetic
vector potential), however, you find that one of these naive degrees
of freedom really doesn't exist; it is unphysical, because it
corresponds to making a gauge transformation.  [Note that a field
theory with massive spin-1 particles is not gauge-invariant.]

Answer two: This is the more interesting answer, and it comes from
group theory, from looking at irreducible representations of the
Poincare group.  One of the Casimir operators of that group is mass,
and the representations with zero and with nonzero mass look very
different.  Regardless of spin, a massless representation has only two
spin states.  

The representations of the Poincare group were worked out by Wigner,
in the 1920s.  You can read his original papers (I've read Bargmann
and Wigner), or you can learn about this result from many other
sources.  I'm fond of Gasiorowicz's book, Elementary Particle Physics;
these issues are also discussed in the ubiquitous Spin, Statistics,
and All That, by Streater and Wightman.
--
Matthew Austern              I dreamt I was being followed by a roving band 
(510) 644-2618               of young Republicans, all wearing the same suit,
matt@physics.berkeley.edu    taunting me and shouting, "Politically correct
austern@theorm.lbl.gov       multiculturist scum!"... They were going to make
austern@lbl.bitnet	     me kiss Jesse Helms's picture when I woke up.