Spin, Statistics, and Reflections, II. Lorentz Invariance
arXiv:math-ph/0512068 · doi:10.1007/s00220-006-0146-6
Abstract
The analysis of the relation between modular PCT-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 $\widetilde{L_+^\uparrow}\cong SL(2,\complex)$ of the restricted Lorentz group 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 PCT-conjugations, and this representation can easily be verified to satisfy the spin-statistics relation.