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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

  1. Is there an easy to understand reason why photons aren't a problem, but a hypothetical particle with spin 3/2 doesn't work?
  2. 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'?
  3. How does supersymmetry help here?
SoVeryCurious
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1 Answers1

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Most of this is covered in this answer: Why do we not have spin greater than 2?

For question 2, this is indeed the case--- you always resolve the composite structure of spin-3/2 particles (which are not gravitinos) at a scale comparable to the mass of the particles. The phenomenon is that the spin-3/2 particle must come in a family of other bound-states, called a Regge trajectory, which unitarizes the scattering by exchange of this particle. Without other degrees of freedom which are at a similar energy, you can't take a pointlike limit. This allows you to predict either new particles related to the original, or a breakup into substructure of some sort.

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Ron Maimon
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