The Role of Relativity in the CPT and Spin–Statistics Theorems
The Role of Relativity in the CPT and Spin–Statistics Theorems
Chapter 2 seeks to understand the role that relativity plays in the CPT and spin–statistics theorems. It first considers the sense in which relativity is not sufficient for CPT invariance and the spin–statistics connection (SSC) by unraveling the different notions of locality (local commutativity, cluster decomposition, causality, and algebraic causality) that appear in these theorems on the one hand, and restricted Lorentz invariance on the other. It then considers the sense in which relativity is not necessary for CPT invariance and the SSC by unpacking the relations among restricted Lorentz invariance, modular covariance, and variants of the latter. The chapter ends by applying the existence problem of Chapter 1 to a critique of an influential claim that maintains that a violation of CPT invariance in an interacting relativistic quantum field theory entails a violation of Lorentz invariance.
Keywords: Local commutativity, cluster decomposition, modular data, geometric modular action
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