(a) Find the simplest irreducible representation of the gravitino, a spin-3/2 particle hypothesized to exist in superstring theory.
(b) Suppose two gravitini collide to form a bound state (a gravitiball). What possible spins could this bound state have?
(c) Suppose you had 10,000 gravitiballs of lowest energy, formed by repeatedly colliding two gravitini together with opposite spins along the z-axis. What must these spin components be if more highest-spin gravitiballs are made than any other kind? Find approximately how many of each spin are made in the sample of 10,000.