Supersymmetry in Elementary Particle Physics · Problem 2.1

Formalism of Supersymmetry

Physics — Particle Physics · susy-commutation-relation-check

Problem

Verify that the supersymmetry transformations (75) for the vector supermultiplet obey the algebra [δξ,δη]=2i(ξ†σˉmη−η†σˉmξ)∂m+δα,[\delta_\xi, \delta_\eta] = 2i\left(\xi^\dagger \bar{\sigma}^m \eta - \eta^\dagger \bar{\sigma}^m \xi\right)\partial_m + \delta_\alpha , where δα\delta_\alpha is a gauge transformation with the gauge parameter α=−2i(ξ†σˉmη−η†σˉmξ)Ama.\alpha = -2i(\xi^\dagger \bar{\sigma}^m \eta - \eta^\dagger \bar{\sigma}^m \xi) A^a_m .

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