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superalgebra

Supersymmetric algebras

• The \(\mathcal{N}=1\) supersymmetry algebra in \(0+1\) dimensions is the de Rham algebra, which consists of
  • the exterior derivative \(d\)
  • its adjoint \(d^{\dagger}\) with respect to the inner product \({\left\langle {a},~{b} \right\rangle} = \int_M \star a \wedge b\),
  • their anticommutator,
  • the Laplacian, which is the Hamiltonian operator of the theory, and commutes with the supercharges).