In the Wikipedia article on the representation theory of the Lorentz group, I've come across the statement:
Fermionic supersymmetry generators transform under one of the (0, 1/2) or (1/2, 0) representations (Weyl spinors).
The four-momentum of a particle (either massless or massive) transforms under the (1/2, 1/2) representation, a four-vector.
What does it mean "to transform" as? I suspect this terminology is borrowed from general relativity where tensors are defined covariantly as "transforms as" and I understand this language. But I do not understand how this is applied in the phrasing above. I suspect it means if we have a principal bundle whose structure group is the Lorentz group then we can build an associated vector bundle using a representation and the language of "transforms as" is really just describing this vector bundle. Am I on the right track?
Also as there is an explicit description of "transforms as" as we have in the covariant description of tensors?
