Editing Spin–statistics theorem (section)

==Relation to representation theory of the Lorentz group==
The [[Lorentz group]] has no non-trivial [[unitary representation]]s of finite dimension. Thus it seems impossible to construct a Hilbert space in which all states have finite, non-zero spin and positive, Lorentz-invariant norm. This problem is overcome in different ways depending on particle spin–statistics.

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.<ref>{{cite book|last1=Peskin|first1=Michael E.|last2=Schroeder|first2=Daniel V.|year=1995|title=An Introduction to Quantum Field Theory|url=https://archive.org/details/introductiontoqu0000pesk|url-access=registration|publisher=[[Addison-Wesley]]|isbn=0-201-50397-2}}</ref>