theorem 106.16 Feynman–Kac

open in the book · parts/11-qft-standard-model/08-path-integral-quantization.tex:939 · p. 2165

Rests on

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 definition 6.6 Continuous map ¶
      - depends_on definition 6.15 Path-connected space ¶
    - depends_on theorem 8.12 Cauchy ¶
      - depends_on equation 8.5 eq:cpx-cr ¶
      - depends_on theorem 7.131 Green ¶
      - proves proof ch:06-complex-analysis@proof-7 ¶
    - 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 ¶
      - depends_on equation 8.6 eq:cpx-contour-integral ¶
      - proves proof ch:06-complex-analysis@proof-4 ¶
    - 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 ¶

Supports

depends_on proposition 106.17 Euclidean time projects onto the ground state ¶
- depends_on phenomenon 106.77 The light hadron spectrum is a prediction of QCD ¶
- depends_on proposition 106.71 The Wilson loop measures the static potential ¶
  - depends_on phenomenon 102.62 The static potential rises linearly ¶
depends_on proposition 106.21 Reflection positivity is the positivity of the Hilbert space ¶
- 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`	→	The Euclidean weight	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:959
`depends_on`	→	Feynman's sum over histories	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:959
`depends_on`	←	Euclidean time projects onto the ground state	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:1021
`depends_on`	←	Reflection positivity is the positivity of the Hilbert space	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:1207
`proves`	←	ch:08-path-integral-quantization@proof-12	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:963