- #1
liorde
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(if I am not even wrong, please let me know )
The generators of the (proper-orthochronous) Lorentz transformations are usually denoted by [itex]{J_{\mu \nu }}[/itex] or by [itex]{M_{\mu \nu }}[/itex]. They consist of angular momentum generators and boost generators.
When discussing spinors, the notation changes to [itex]{S_{\mu \nu }}[/itex] (which is equal to the commutator of gamma matrices).
I am trying to understand if the change of notation reflects a difference between [itex]S[/itex] and [itex]J[/itex], or if it just a change of convention.
Is there any sense in which [itex]{S_{\mu \nu }}[/itex] is just spin while [itex]{J_{\mu \nu }}[/itex] is angular momentum?
Is there any sense in which [itex]{S_{\mu \nu }}[/itex] generates inner transformations while [itex]{J_{\mu \nu }}[/itex] does not?
Thanks
The generators of the (proper-orthochronous) Lorentz transformations are usually denoted by [itex]{J_{\mu \nu }}[/itex] or by [itex]{M_{\mu \nu }}[/itex]. They consist of angular momentum generators and boost generators.
When discussing spinors, the notation changes to [itex]{S_{\mu \nu }}[/itex] (which is equal to the commutator of gamma matrices).
I am trying to understand if the change of notation reflects a difference between [itex]S[/itex] and [itex]J[/itex], or if it just a change of convention.
Is there any sense in which [itex]{S_{\mu \nu }}[/itex] is just spin while [itex]{J_{\mu \nu }}[/itex] is angular momentum?
Is there any sense in which [itex]{S_{\mu \nu }}[/itex] generates inner transformations while [itex]{J_{\mu \nu }}[/itex] does not?
Thanks