lemma 109.25 Positivity of the cone pairing

open in the book · parts/11-qft-standard-model/11-axiomatic-qft.tex:834 · p. 2302

Rests on

depends_on notation 109.8 Conventions of this chapter ¶
proves proof ch:11-axiomatic-qft@proof-7 ¶

Supports

depends_on theorem 109.26 Analyticity in the forward tube ¶
- depends_on proposition 109.23 Uniqueness of the vacuum equals clustering ¶
- depends_on theorem 109.28 Bargmann–Hall–Wightman; imported ¶
  - 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 ¶ ↺
- depends_on theorem 109.4 Haag ¶
  - depends_on corollary 109.5 The interaction picture does not exist ¶
- depends_on theorem 109.34 Reeh–Schlieder ¶
  - depends_on corollary 109.35 No local operator annihilates the vacuum ¶
  - depends_on theorem 109.49 Spin and statistics ¶ ↺
  - depends_on theorem 109.72 Tomita–Takesaki; imported ¶
    - depends_on proposition 109.74 The vacuum is thermal in a wedge ¶
    - depends_on theorem 109.73 Bisognano–Wichmann; imported ¶
      - depends_on proposition 109.74 The vacuum is thermal in a wedge ¶ ↺

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`	→	Conventions of this chapter	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:842
`depends_on`	←	Analyticity in the forward tube	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:868
`proves`	←	ch:11-axiomatic-qft@proof-7	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:845