I'm reading Alvarez-Gaume review on Seiberg-Witten theory: http://arxiv.org/abs/hep-th/9701069.(adsbygoogle = window.adsbygoogle || []).push({});

Around page 23 you can find the following claim:

"This is a Clifford algebra with 2N generators and has a 2N-dimensional representation. From the point of view of the angular momentum algebra, [itex]a^I[/itex] is a rising operator and [itex](a^I)^\dagger[/itex] is a lowering operator for the helicity of massless states"

The definitions of [itex]a^I[/itex] and [itex](a^I)^\dagger[/itex] are given a few lines above. How to see that the first raise helicity while the second lowers it?

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# Reps of the SUSY algebra: raising and lowering operators

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