theorem 109.28 Bargmann–Hall–Wightman; imported

open in the book · parts/11-qft-standard-model/11-axiomatic-qft.tex:923 · p. 2303

Rests on

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 ¶

Supports

depends_on corollary 109.43 Total inversion is automatic ¶
- depends_on theorem 109.44 Jost ¶
  - depends_on corollary 109.45 Locality implies $PCT$ ¶
- depends_on theorem 109.49 Spin and statistics ¶
  - depends_on corollary 109.50 The connection between spin and statistics ¶
depends_on theorem 109.49 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
`cites`	→	A theorem on invariant analytic functions with applications to relativistic quantum field theory	derived	parts/11-qft-standard-model/11-axiomatic-qft.tex:936
`depends_on`	→	The complex Lorentz group	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:937
`depends_on`	→	Properties of the Wightman functions	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:937
`depends_on`	→	Analyticity in the forward tube	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:937
`depends_on`	←	Total inversion is automatic	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:1324
`depends_on`	←	Spin and statistics	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:1532
`proves`	←	ch:11-axiomatic-qft@proof-9	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:941