- #1
Elwin.Martin
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Alright, so I was reading Ryder and he defines the generator corresponding to [itex]a^{\alpha}[/itex] as the following
[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-v2)-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:
Kx=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.
[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-v2)-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:
Kx=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.