Reflection Positive Hilbert Spaces Associated to Local Positive Definite Z_2^n-Superfunctions

reflection positivity is a basic concept in constructive quantum field theory [1]. The underlying framework of reflection positivity is reflection positive Hilbert space, introduced in [4]. This is a triple (E, E+, θ), where E is a Hilbert space, θ : E → E isa unitary involution and E+ is a closed subspace of E which is θ_x0002_positive in the sense that the hermitian form θu, v is positive semidefinite on E+. In this paper we construct a reflection posi_x0002_tive Hilbert space associated to a positive definite function definedlocally on a Zn2-graded Lie supergroup.