PCT, spin and statistics and all that
Abstract
PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.
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The construction of H_BU is analogous to the construction of a quantum field theory Hilbert space from correlation functions via Wightman or Osterwalder-Schrader reconstruction, with Z[J] corresponding to smeared local operators inserted in the Euclidean past and inner products of finitely many operator insertions given by Euclidean Wightman functions.
“The above construction of H BU is very similar to the construction of the Hilbert space of a quantum field theory from its correlation functions in the Wightman [79] or Osterwalder-Schrader (see Theorem 3-7 of [80,81]) reconstuction theorems.”
From Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information (2020) · cites this paper as [80]
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- Authors
- Streater, R. F., & Wightman, A. S.
- Venue
- Princeton University Press eBooks
- Publisher
- Princeton University Press
- Published
- 2001-12-31
- OpenAlex
- W1504171473
- Cited by
- 1,784
- References
- 0
- Citations by year
- 2026: 11 · 2025: 16 · 2024: 28 · 2023: 27 · 2022: 34 · 2021: 65 · 2020: 36 · 2019: 84 · 2018: 37 · 2017: 41 · 2016: 46 · 2015: 54 · 2014: 43 · 2013: 42 · 2012: 41
- FWCI
- 11.64
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Princeton University Press eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- spin-statistics theorem, axiomatic field theory, quantized fields, mathematical foundations of quantum field theory
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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