The CPT and Spin–Statistics Theorems in Relativistic Quantum Field Theories
The CPT and Spin–Statistics Theorems in Relativistic Quantum Field Theories
Chapter 1 first reviews how CPT invariance and the spin–statistics connection are typically represented in relativistic quantum field theories (RQFTs). It then reviews four distinct versions of the CPT and spin–statistics theorems: the Wightman axiomatic approach, an approach due to Steven Weinberg, the Lagrangian approach, and the algebraic approach. The differences among these approaches are summarized, and they are then identified with one of two positions: on a first gloss, pragmatist approaches trade mathematical rigor for the ability to formulate realistic interacting RQFTs, whereas purist approaches trade the ability to formulate realistic interacting RQFTs for mathematical rigor. The chapter ends with a discussion of the “existence problem” as a more nuanced way of making the distinction between pragmatism and purity than a simple appeal to mathematical rigor.
Keywords: Wightman axiomatic quantum field theory, S-matrix, algebraic QFT, renormalization group, perturbation theory, convergence
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