Spin, Statistics, and Reflections, I. Rotation Invariance
Bernd Kuckert
TL;DR
This paper models the universal covering of SO(3) as a reflection group and explores how modular P_1CT-symmetry in relativistic quantum fields leads to a representation satisfying the spin-statistics relation.
Contribution
It introduces a representation of the universal covering of SO(3) using reflection groups and modular symmetry, linking it to the spin-statistics relation in quantum fields.
Findings
Representation of G_R constructed via modular P_1CT-operators
Satisfaction of Pauli's spin-statistics relation
Connection between reflection symmetry and quantum field properties
Abstract
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 P_1CT-symmetry (Bisognano, Wichmann, 1975, 1976, and Guido, Longo, [funct-an/9406005]). This symmetry is used to construct a representation of G_R by pairs of modular P_1CT-operators. The representation thus obtained satisfies Pauli's spin-statistics relation.
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