theorem 109.49 Spin and statistics

open in the book · parts/11-qft-standard-model/11-axiomatic-qft.tex:1523 · p. 2310

Rests on

depends_on corollary 109.43 Total inversion is automatic ¶
- depends_on lemma 109.42 Total inversion is a complex Lorentz transformation ¶
  - depends_on definition 109.27 The complex Lorentz group ¶
  - depends_on definition 39.5 Orthochronous Lorentz group ¶
    - depends_on definition 39.1 Lorentz group ¶
      - depends_on definition 38.6 Minkowski metric and interval ¶
    - depends_on equation 39.3 eq:mink-noncompact ¶
      - step_from equation 39.2 eq:mink-lorentz-condition ¶
  - proves proof ch:11-axiomatic-qft@proof-14 ¶
- depends_on theorem 109.28 Bargmann–Hall–Wightman; imported ¶
  - depends_on definition 109.27 The complex Lorentz group ¶ ↺
  - depends_on proposition 109.20 Properties of the Wightman functions ¶
    - depends_on axiom 109.13 Covariance ¶
    - depends_on axiom 109.12 Fields ¶
    - depends_on axiom 109.14 Local commutativity ¶
    - depends_on axiom 109.10 Spectrum condition ¶
    - depends_on axiom 109.9 Relativistic states ¶
    - depends_on axiom 109.11 Unique vacuum ¶
    - proves proof ch:11-axiomatic-qft@proof-4 ¶
  - depends_on theorem 109.26 Analyticity in the forward tube ¶
    - depends_on equation 109.16 eq:axqft-wightman-support ¶
    - depends_on lemma 109.25 Positivity of the cone pairing ¶
      - depends_on notation 109.8 Conventions of this chapter ¶
      - proves proof ch:11-axiomatic-qft@proof-7 ¶
    - proves proof ch:11-axiomatic-qft@proof-8 ¶
  - proves proof ch:11-axiomatic-qft@proof-9 ¶
- depends_on theorem 109.30 Jost; imported ¶
  - depends_on definition 109.27 The complex Lorentz group ¶ ↺
  - depends_on definition 109.29 Jost points ¶
- proves proof ch:11-axiomatic-qft@proof-15 ¶
depends_on theorem 109.28 Bargmann–Hall–Wightman; imported ¶ ↺
depends_on theorem 109.34 Reeh–Schlieder ¶
- depends_on axiom 109.15 Cyclicity of the vacuum ¶
- depends_on axiom 109.14 Local commutativity ¶ ↺
- depends_on theorem 109.26 Analyticity in the forward tube ¶ ↺
- proves proof ch:11-axiomatic-qft@proof-11 ¶
proves proof ch:11-axiomatic-qft@proof-19 ¶
proves proof ch:11-axiomatic-qft@proof-20 ¶

Supports

depends_on corollary 109.50 The connection between spin and statistics ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Total inversion is automatic	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:1532
`depends_on`	→	Bargmann–Hall–Wightman; imported	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:1532
`depends_on`	→	Reeh–Schlieder	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:1532
`depends_on`	←	The connection between spin and statistics	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:1628
`proves`	←	ch:11-axiomatic-qft@proof-19	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:1536
`proves`	←	ch:11-axiomatic-qft@proof-20	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:1604