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## Main Question or Discussion Point

I want to prove that:

[tex] [J_1,G_1] = 0 [/tex]

Where J is the rotation operator and G is the boost operator (subscript refers to the axis).

I am using the Jacobi identity:

[tex] [[J_1,J_2],G_3] = [[G_3,J_2],J_1] +[[J_1,G_3],J_2] [/tex]

Using other identities, I got:

[tex] [J_3,G_3] = [G_2,J_2] - [G_1,J_1] [/tex]

Now I'm not sure what to do, can someone help?

[tex] [J_1,G_1] = 0 [/tex]

Where J is the rotation operator and G is the boost operator (subscript refers to the axis).

I am using the Jacobi identity:

[tex] [[J_1,J_2],G_3] = [[G_3,J_2],J_1] +[[J_1,G_3],J_2] [/tex]

Using other identities, I got:

[tex] [J_3,G_3] = [G_2,J_2] - [G_1,J_1] [/tex]

Now I'm not sure what to do, can someone help?