Abstract. An algebraic supersymmetric quantum field theory in a thermal background is supposed to provide the following data - a Z₂-graded C^*-dynamical system, a (possibly unbounded) self-adjoint graded-KMS functional on it and a superderivation of the algebra (the supersymmetry generator), whose square is the generator of the evolution group. It is shown how one can reconstruct canonically from this data a representation of the theory in a Z₂-graded Hilbert space, so that the grading of the Hilbert space is in some natural way compatible with the functional. The superderivation is implemented as a graded commutator with an unbounded odd operator (supercharge). The modular conjugation operator plays a crucial role in this reconstruction.

Full-text: PDF