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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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CPT Invariance and the Spin–Statistics Connection in Non-Relativistic Quantum Field Theories

CPT Invariance and the Spin–Statistics Connection in Non-Relativistic Quantum Field Theories

Chapter:
(p.82) 3 CPT Invariance and the Spin–Statistics Connection in Non-Relativistic Quantum Field Theories
Source:
CPT Invariance and the Spin-Statistics Connection
Author(s):

Jonathan Bain

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198728801.003.0004

Chapter 3 addresses the question “Why are CPT invariance and the spin–statistics connection not derivable properties in non-relativistic quantum field theories (NQFTs)?” It first describes the difference between relativistic quantum field theories (RQFTs) and NQFTs in terms of spacetime structure. It then considers how to formulate NQFTs in each of the approaches reviewed in Chapter 1: the axiomatic approach, Weinberg’s approach, the Lagrangian approach, and the algebraic approach. Answers to the initial question are then framed within each of these approaches. The chapter ends with an analysis of the intertheoretic relations between RQFTs on the one hand, and NQFTs on the other. In particular, it considers how a speed-space contraction of the Poincaré group can provide the basis for an intertheoretic relation that maps the kinematical structure of RQFTs into the kinematical and (aspects of) the dynamical structure of NQFTs.

Keywords:   Minkowski spacetime, classical spacetime, non-relativistic quantum field theory, Bronstein cube, speed-space contraction

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