Spin, statistics, and reflections - II. Lorentz invariance

The analysis of the relation between modular P1CT-symmetry - a consequence of the Unruh effect - and Pauli's spin-statistics relation is continued. The result in the predecessor to this article is extended to the Lorentz symmetric situation. A model G(L) of the universal covering L-+(up arrow)congruent to SL(2, C) of the restricted Lorentz group L-+(up arrow) is modelled as a reflection group at the classical level. Based on this picture, a representation of G(L) is constructed from pairs of modular P1CT-conjugations, and this representation can easily be verified to satisfy the spin-statistics relation.