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Introduction to Physical Content from Adjoint Representations
In particle Physics it's usual to write the physical content of a Theory in adjoint representations of the Gauge group. For example:
$24\rightarrow (8,1)_0\oplus (1,3)_0\oplus (1,1)_0\oplus ...
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A nice overview (and maybe derivation) of the Poincaré transformations of the Vector Spherical Harmonics
With $Y_{lm}(\vartheta,\varphi)$ being the Spherical Harmonics and $z_l^{(j)}(r)$ being the Spherical Bessel functions ($j=1$), Neumann functions ($j=2$) or Hankel functions ($j=3,4$) defining ...
