# Help with Supersymmetry

1. Jun 6, 2006

### AlphaNumeric

It's been bugging my for ages, but I cannot see to show the following supersymmetry algebra :

$$\delta_{\epsilon} X^{\mu} = \bar{\epsilon}\bar{\psi}$$
$$\delta_{\epsilon} \psi^{\mu} = \rho .\partial X^{\mu}\epsilon$$

Using these show that

$$[\delta_{\epsilon_{1}},\delta_{\epsilon_{2}}]X^{\mu} = 2\bar{\epsilon}_{1}\rho^{\alpha}\epsilon_{2}\partial_{\alpha}X^{\mu}$$
$$[\delta_{\epsilon_{1}},\delta_{\epsilon_{2}}]\psi^{\mu} = 2\bar{\epsilon}_{1}\rho^{\alpha}\epsilon_{2}\partial_{\alpha}\psi^{\mu}$$

using $$\rho . \partial \psi^{\mu}=0$$ and $$\epsilon$$ being a Grassman spinor.

I can do the first one but I cannot do the second one. Every textbook I check just says "It can be shown that..." but I can't actually show it!! :uhh: