CPT Invariance, the Spin-Statistics Connection, and the Ontology of Relativistic Quantum Field Theories

Lawrence Paul Horwitz, Rafael I Arshansky

Enrico Santamato, F. De Martini

Aaron Bennett

Jonathan Bain

Chapter 5 addresses the question, “What explains CPT invariance and the spin–statistics connection (SSC)?” It first considers why we should care about explaining CPT invariance and the SSC. It then argues that the CPT and spin–statistics theorems cannot be said to provide the sought after explanations. It offers instead an explanation of the SSC in interacting non-relativistic theories. This explanation explains by virtue of a derivation from non-fundamental principles in non-interacting relativistic quantum field theories (RQFTs), and an explication of intertheoretic relations between interacting RQFTs, non-interacting RQFTs, and interacting non-relativistic theories. The chapter ends by arguing that the presence of both the SSC and CPT invariance in realistic interacting RQFTs cannot be explained by even this type of explanation, and that currently, the existence problem precludes a full understanding of these properties in realistic interacting RQFTs.

Jonathan Bain

This book seeks to answer the question "What explains CPT invariance and the spin-statistics connection?" These properties play foundational roles in relativistic quantum field theories (RQFTs), are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and Spin-Statistics theorems; but, the author argues, these theorems cannot be said to explain these properties, at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work towards an understanding of CPT invariance and the spin-statistics connection by first providing an analysis of the necessary and sufficient conditions for these properties, and second by advocating a particular account of explanation appropriate for this context.

Iu. M. Shirokov