Spin, Statistics, and Reflections I. Rotation Invariance

The universal covering of SO(3) is modelled as a reflection group G_R in a representation independent fashion. For relativistic quantum fields, the Unruh effect of vacuum states is known to imply an intrinsic form of reflection symmetry, which is referred to as modular P₁CT-symmetry [1, 2, 11]. This symmetry is used to construct a representation of G_R by pairs of modular P₁CT-operators. The representation thus obtained satisfies Pauli’s spin-statistics relation. Communicated by Klaus Fredenhagen submitted 01/12/04, accepted 06/12/04