The simplest superalgebras in two, three, four and five dimensions Original Research Article

The simplest super-Poincaré algebras in two through five space–time dimensions with varying signatures are determined. The possibility of employing more than one definition of charge conjugation is considered. The Hilbert space associated with the Fermionic creation and annihilation operators is examined in each case to see what conditions must be met for it to be positive definite. Representations of the algebras are provided in a number of the spaces considered.