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.
Read more about this topic: Spin-statistics Theorem
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