- #1

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## Main Question or Discussion Point

Ok, I'm trying to teach myself about supersymmetry, using Weinberg III. My learning style is I don't really read things I just kind of infer what the author means. So I need clarification on a lot.

Lets start with the basics, from a mathematical point of view.

Where I'm at is at Haag Lopusanzski Sohnius theorem:

Now basically how I see this is as [tex]SO_ + (1,3) \cong \frac{{SL(2,\mathbb{C})}}{{Z_2 }}[/tex] So [tex]SO_ + (1,3)[/tex] is not simply connected, but has a [tex]{Z_2 }[/tex] grading. Your representation can be chosen so that [tex]{\mathbf{U}}(\bar \Lambda ){\mathbf{U}}(\Lambda ) = \pm {\mathbf{U}}(\bar \Lambda \Lambda )[/tex]. Where the + and - depend on whether you are talking about integer spin or half integer spin. Now my question is can I obtain Haag and Lopusanzski's results by working out the lie algebras of [tex]{\mathbf{U}}(\bar \Lambda ){\mathbf{U}}(\Lambda ) = \pm {\mathbf{U}}(\bar \Lambda \Lambda )[/tex]?

Lets start with the basics, from a mathematical point of view.

Where I'm at is at Haag Lopusanzski Sohnius theorem:

Now basically how I see this is as [tex]SO_ + (1,3) \cong \frac{{SL(2,\mathbb{C})}}{{Z_2 }}[/tex] So [tex]SO_ + (1,3)[/tex] is not simply connected, but has a [tex]{Z_2 }[/tex] grading. Your representation can be chosen so that [tex]{\mathbf{U}}(\bar \Lambda ){\mathbf{U}}(\Lambda ) = \pm {\mathbf{U}}(\bar \Lambda \Lambda )[/tex]. Where the + and - depend on whether you are talking about integer spin or half integer spin. Now my question is can I obtain Haag and Lopusanzski's results by working out the lie algebras of [tex]{\mathbf{U}}(\bar \Lambda ){\mathbf{U}}(\Lambda ) = \pm {\mathbf{U}}(\bar \Lambda \Lambda )[/tex]?