theorem 109.73 Bisognano–Wichmann; imported

open in the book · parts/11-qft-standard-model/11-axiomatic-qft.tex:2305 · p. 2319

Rests on

depends_on theorem 109.46 Existence of the $PCT$ operator ¶
- depends_on axiom 109.13 Covariance ¶
- depends_on axiom 109.9 Relativistic states ¶
- depends_on definition 109.40 The $PCT$ condition ¶
- proves proof ch:11-axiomatic-qft@proof-18 ¶
depends_on theorem 109.72 Tomita–Takesaki; 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 ¶
    - 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-11 ¶

Supports

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
`cites`	→	On the duality condition for a Hermitian scalar field	derived	parts/11-qft-standard-model/11-axiomatic-qft.tex:2318
`cites`	→	On the duality condition for quantum fields	derived	parts/11-qft-standard-model/11-axiomatic-qft.tex:2318
`depends_on`	→	Existence of the $PCT$ operator	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:2319
`depends_on`	→	Tomita–Takesaki; imported	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:2319
`depends_on`	←	The vacuum is thermal in a wedge	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:2333