Regarding representations of the Lorentz group

[Kontilera]

Hello! I'm currently reading Peskin and Schroeder and am curious about a qoute on page 38, which concerns representations of the Lorentz group.

”It can be shown that the most general nonlinear transformation laws can be built from these linear transformations, so there is no advantage in considering transformations more general than (3.8.).”

Where (3.8.) is,
$$\Phi_a(x) \rightarrow M_{ab}(\Lambda)\Phi_b(\Lambda^{-1}x).$$

If anybody has time to expand this claim a bit I would be really happy, otherwise just give me a referens.

Thanks!

 

[dextercioby]

It's nonsense to discuss about nonlinear transformations in the first place, so I can't comment any further.

 

[Kontilera]

Why is it nonsense? Would you like to explain?