Alright, so I was reading Ryder and he defines the generator corresponding to [itex]a^{\alpha}[/itex] as the following(adsbygoogle = window.adsbygoogle || []).push({});

[itex]X_{\alpha}[/itex]=[itex]\frac{\partial x'^{\mu}}{\partial a^{\alpha}}[/itex][itex]\frac{\partial}{\partial x^{\mu}}[/itex] ([itex]\alpha =1,...r[/itex]) for r-parameter group of transformations

Now this makes sense for

[itex]a^{\alpha}[/itex]=θ and we get Rotation...but he then says he applies it to "pure" Lorentz transformations:

x'=γ(x+vt)

y'=y

z'=z

t'=γ(t+vx)

γ=(1-v^{2})^{-1/2}

and I'm not even sure what parameter he's going after here ._. I feel really dumb asking, but what does he do to get from there to here:

K_{x}=i[itex]\left(t\frac{\partial}{\partial x}+x\frac{\partial}{\partial t}\right)[/itex]

It feels like he loses a factor of γ somewhere or something, too.

Thanks for any and all help, this has been bothering me for a while.

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# Poincare Group and Generators

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