proposition 106.21 Reflection positivity is the positivity of the Hilbert space

open in the book · parts/11-qft-standard-model/08-path-integral-quantization.tex:1196 · p. 2168

Rests on

depends_on equation 106.30 eq:pathint-reflection-positivity ¶
depends_on theorem 106.16 Feynman–Kac ¶
- depends_on proposition 106.13 The Euclidean weight ¶
  - depends_on definition 106.12 Euclidean time ¶
  - proves proof ch:08-path-integral-quantization@proof-10 ¶
- depends_on theorem 106.3 Feynman's sum over histories ¶
  - depends_on equation 106.1 eq:pathint-propagator-def ¶
  - depends_on lemma 106.1 The short-time kernel ¶
    - depends_on corollary 8.15 Deformation of contours ¶
      - depends_on definition 6.17 Simply connected space ¶
      - depends_on theorem 8.12 Cauchy ¶
      - proves proof ch:06-complex-analysis@proof-9 ¶
    - depends_on lemma 106.2 Gaussian integrals ¶
      - depends_on equation 17.42 eq:ft-gaussian ¶
      - depends_on lemma 8.9 ML estimate ¶
      - proves proof ch:08-path-integral-quantization@proof-2 ¶
    - proves proof ch:08-path-integral-quantization@proof-1 ¶
  - proves proof ch:08-path-integral-quantization@proof-3 ¶
- proves proof ch:08-path-integral-quantization@proof-12 ¶
proves proof ch:08-path-integral-quantization@proof-15 ¶

Supports

depends_on proposition 109.82 Wilson's action is reflection positive ¶

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`	→	eq:pathint-reflection-positivity	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:1207
`depends_on`	→	Feynman–Kac	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:1207
`depends_on`	←	Wilson's action is reflection positive	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:2576
`proves`	←	ch:08-path-integral-quantization@proof-15	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:1210