Relation to representation theory of the Lorentz group 

                                   Since the Lorentz group has no non-trivial unitary representation of finite dimension, it naively seems that one cannot construct a state with finite, non-zero spin and positive, Lorentz-invariant norm.

For a state of integer spin the negative norm states (known as "unphysical polarization") are set to zero, which makes the use of gauge symmetry necessary.

For a state of half-integer spin the argument can be circumvented by having fermionic statistics.