Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Supersymmetry in Elementary Particle Physics · Problem 2.3
Formalism of Supersymmetry
Physics — Particle Physics · susy-commutation-relation-psi
Problem Using the Fierz identity
η α ξ β † = − 1 2 ( ξ † σ ˉ m η ) σ α β m , \eta_\alpha \xi^\dagger_\beta = -\frac{1}{2}(\xi^\dagger \bar{\sigma}^m \eta)\sigma^m_{\alpha\beta} , η α ξ β † = − 2 1 ( ξ † σ ˉ m η ) σ α β m , [ δ ξ , δ η ] [\delta_\xi, \delta_\eta] [ δ ξ , δ η ] ψ \psi ψ [ δ ξ , δ η ] = 2 i ( ξ † σ ˉ m η − η † σ ˉ m ξ ) ∂ m . [\delta_\xi, \delta_\eta] = 2i\left(\xi^\dagger \bar{\sigma}^m \eta - \eta^\dagger \bar{\sigma}^m \xi\right)\partial_m . [ δ ξ , δ η ] = 2 i ( ξ † σ ˉ m η − η † σ ˉ m ξ ) ∂ m . Browse the problem library