Operator-theoretical analysis of a representation of a supersymmetry algebra in Hilbert space

Abstract

Operator-theoretical analysis is made on (unbounded) representations, in Hilbert spaces, of a supersymmetry (SUSY) algebra coming from a supersymmetric quantum field theory in two-dimensional space–time. A basic idea for the analysis is to apply the theory of strongly anticommuting self-adjoint operators. A theorem on integrability of a representation of the SUSY algebra is established. Moreover, it is shown that strong anticommutativity of self-adjoint operators is a natural and suitable concept in analyzing representations of the SUSY algebra in Hilbert space.