Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 68 / 1 / e

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- Solution e

Solution

The supersymmetry algebra closes on spacetime translations. Its supercharges are Weyl spinors, and

{Q_{α}, \overset{ˉ}{Q}_{\dot{β}}} = 2 σ_{α \dot{β}}^{μ} P_{μ} .

Thus the composition of two odd supersymmetry transformations moves the spacetime argument. The generators also change spin and connect bosons with fermions. They extend the Poincaré group to the Super-Poincaré group, rather than forming an internal symmetry that commutes with spacetime transformations.

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