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Supersymmetry

Postulates a symmetry in nature that relates bosons and fermions, predicting the existence of partner particles for all known particles, addressing the hierarchy problem.
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The statement of the theorem

Define the supercharge operator QQ and the super-Poincaré algebra by the anti-commutation relation: {QA,QˉB}=2×(γμPμ)δAB \{ Q_A, \bar{Q}_B \} = 2 \times (\gamma^{\mu} P_{\mu}) \delta_{AB} . The action for a supermultiplet Φ\Phi is given by the superfield integral: S=∫d4x(12(∂μΦ)(∂μΦ)+V(Φ)) S = \int d^4x \left( \frac{1}{2} \left( \partial_{\mu} \Phi \right) \left( \partial^{\mu} \Phi \right) + V(\Phi) \right) where the transformation relates bosonic components ϕ\phi and fermionic components ψ\psi via the supercovariant derivative DαD_{\alpha}.