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Hi all I'm new on this forum. I'm here since I'm working with n-extended susy and R-sym and I don't know how to calculate a commutator. First of all I introsuce my notation:

[tex] \mu_A T^A [/tex] is a potential cupled to R-sym generator

[tex] \mu_{\alpha i} [/tex] is a superpotential cupled to supercharges

[tex] (-1)^F = e^{2 \pi i J_z} [/tex] counts number of fermions

[tex] \{ Q_{\alpha}^i ; \bar{Q}_{\dot{\alpha}j} \} = 2 \sigma_{ \alpha \dot{\aplha}}^\mu P_\mu \delta^i_j [/tex]

(I hope you see it right since on my pc I don't see curly bracket of anticommutator and just one alpha dot under sigma, but this is just the super algebra)

and spinorial indices are raised and lowered with

[tex] \varepsilon^{12}=\varepsilon_{21}=\varepsilon^{\dot{1}\dot{2}}=\varepsilon_{\dot{2}\dot{1}}=1 [/tex]

Now what I have to compute is

[tex] \left[(-1)^F ; e^{\mu_A T^A + \mu^{\alpha i} Q_{\alpha}^i + \bar{\mu}_{\dot{\alpha}j} \bar{Q}^{\dot{\alpha}j} } \right] [/tex]

How can I do? Thanks for advices!

[tex] \mu_A T^A [/tex] is a potential cupled to R-sym generator

[tex] \mu_{\alpha i} [/tex] is a superpotential cupled to supercharges

[tex] (-1)^F = e^{2 \pi i J_z} [/tex] counts number of fermions

[tex] \{ Q_{\alpha}^i ; \bar{Q}_{\dot{\alpha}j} \} = 2 \sigma_{ \alpha \dot{\aplha}}^\mu P_\mu \delta^i_j [/tex]

(I hope you see it right since on my pc I don't see curly bracket of anticommutator and just one alpha dot under sigma, but this is just the super algebra)

and spinorial indices are raised and lowered with

[tex] \varepsilon^{12}=\varepsilon_{21}=\varepsilon^{\dot{1}\dot{2}}=\varepsilon_{\dot{2}\dot{1}}=1 [/tex]

Now what I have to compute is

[tex] \left[(-1)^F ; e^{\mu_A T^A + \mu^{\alpha i} Q_{\alpha}^i + \bar{\mu}_{\dot{\alpha}j} \bar{Q}^{\dot{\alpha}j} } \right] [/tex]

How can I do? Thanks for advices!

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