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CPT Invariance and the Spin-Statistics Connection$
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Jonathan Bain

Print publication date: 2016

Print ISBN-13: 9780198728801

Published to Oxford Scholarship Online: May 2016

DOI: 10.1093/acprof:oso/9780198728801.001.0001

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The Role of Relativity in the CPT and Spin–Statistics Theorems

The Role of Relativity in the CPT and Spin–Statistics Theorems

Chapter:
(p.46) 2 The Role of Relativity in the CPT and Spin–Statistics Theorems
Source:
CPT Invariance and the Spin-Statistics Connection
Author(s):

Jonathan Bain

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198728801.003.0003

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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