I am in undergraduate quantum mechanics, and the TA made an off-hand comment that currently no one knows how to describe fundamental particles with spin > 1 without supersymmetry. I was curious and tried to look up info on this, and wikipedia does make some comments about troubles with spin 3/2 http://en.wikipedia.org/wiki/Rarita%E2%80%93Schwinger_equation
So my questions are
- Is there an easy to understand reason why photons aren't a problem, but a hypothetical particle with spin 3/2 doesn't work?
- Does this also mean there are troubles explaining 3/2 composite particles in a low energy regime where we can treat the composite as strongly bound / 'fundamental'?
- How does supersymmetry help here?