Undergrad Wigner's Theorem That All Fields Must Be Tensors

[bhobba]

I know in 1939 Wigner published a theorem that all fields must be tensors from a couple of books, but can't find the proof anywhere. That obviously is an important result so does anyone know where I can find the proof? Another I haven't seen the proof of is the no interaction theorem. I wish someone would publish book with these kind of results are in one place.

Thanks
Bill

 

[vanhees71]

Just read the original paper. It's a milestone in relativistic (Q)FT and, imho, also in scientific writing:

E. P. Wigner, On Unitary Representations of the Inhomgeneous Lorentz Group, Annals of Mathematics 40 (1939) 149.
https://dx.doi.org/10.1016/0920-5632(89)90402-7

Of course, in the context of QT, it's not the Poincare group (or "inhomogeneous Lorentz group") as Wigner writes in the title but the (central extensions of) the covering group. Since there are no non-trivial central extensions (see Weinberg's QT of Fields, Vol. I) the only thing is that the proper orthochronous Lorentz groiup as a subgroup of the Poincare group is to be substituted by its covering group, which is $\mathrm{SL}(2,\mathbb{C})$ (with the $\mathrm{SU}(2)$ as a subgroup reprenting spatial rotations of course as in non-relativistic QT). The importance of this is that within quantum theory you can have half-integer spin (or helicities for massless particles) and fermions.